SecProbe.io

CORRESP
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CORRESP

 1095 Avenue of the Americas

 New York, NY
10036-6797

 +1 212 698 3500 Main

 +1 212 698 3599 Fax

www.dechert.com

 RICHARD HOROWITZ

 richard.horowitz@dechert.com

+1 212 698 3525 Direct

 +1 212 698 0452 Fax

 August 18, 2020

 Alberto
H. Zapata, Esq.

 Senior Counsel

 Division of Investment
Management

 Securities and Exchange Commission

 100 F Street,
N.E.

 Washington, D.C. 20549-0504

Re:
 Conversus StepStone Private Markets

Filing No: 333-239638; 811-23480

Dear Mr. Zapata:

 We are writing in
response to comments provided via electronic mail on July 31, 2020 with respect to the registration statement on Form N-2 (the “Registration Statement”) under the Securities Act of 1933, as
amended (the “1933 Act”) and the Investment Company Act of 1940, as amended (the “1940 Act”), filed on July 2, 2020 on behalf of Conversus StepStone Private Markets (the “Fund”), a
closed-end management investment company. The Fund has considered these comments and has authorized us to make the responses discussed below on its behalf.

On behalf of the Fund, set forth below are the SEC staff’s comments along with our responses to or any supplemental explanations of such
comments, as requested.

1.
 General Comments

Comment 1(a). The filing contains blanks for missing disclosure. Please ensure that all missing information is included in a pre-effective amendment responding to these comments, including completed registration fee information.

Response 1(a). We hereby confirm that all missing information will be included in a
pre-effective amendment responding to your comments, including the completed registration fee information.

Comment 1(b). Please tell us if you have presented or will present any “test the waters” materials to potential investors in
connection with this offering. If so, please provide us with copies of such materials.

 Response 1(b). We respectfully acknowledge your comment. We hereby
confirm that there will be no “test the waters” materials in connection with this offering.

 Comment 1(c). In April, the
Commission adopted rules related to securities offering reform for closed-end investment companies. See IC-33836, Apr. 8, 2020. Many of those rule and form changes are
effective August 1, 2020. Please make all necessary changes to the registration statement to comply with applicable changes. Specific reference to form item and instruction numbers cited below correspond to the version of Form N-2 effective August 1, 2020.

 Response 1(c). We respectfully acknowledge
your comment and hereby confirm that we have made necessary revisions to comply with the applicable changes to Form N-2.

Comment 1(d). Conversus StepStone Private Markets currently has an effective registration statement on Form
N-2 under the 1940 Act only. Please clarify, supplementally, whether any classes of Shares have been sold pursuant to that registration statement and whether, once the filing registering the Fund’s shares
under the 33 Act is effective, shares not registered under the 33 Act will be in the market.

 Response 1(d). We
respectfully acknowledge your comment. As of the date hereof, the Fund has not sold any classes of shares other than $100,000 of shares of a single class to the seed investor in order to comply with the requirements of Rule 14(a) of the 1940 Act,
and has not commenced operations. The Fund intends to have an initial closing (an “Initial Closing”) prior to the effective date of its 1933 Act registration statement, issuing shares in accordance with its existing private placement,
which shares would be subject to repurchase pursuant to the Fund’s quarterly share repurchase program or transfer pursuant to the Fund’s limitations on transfer. As disclosed in the registration statement, the Fund is not listed on any
exchange and no public secondary market for the Fund’s shares is expected to develop. Accordingly, we do not believe that unregistered shares of the Fund will be present in the market in a meaningful way. In any case, the restricted shares will
bear appropriate legends on the books of the transfer agent.

2.
 Facing Sheet

Comment 2(a). Please submit a new N-2 facing sheet comporting with Form N-2 effective August 1, 2020; check all applicable boxes.

 Response 2(a).
The facing sheet has been revised accordingly.

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3.
 Cover Page

Comment 3(a). Please consider whether the word “Fund” should be added to the registrant’s legal name in order to clarify for
retail investors the nature of the financial instrument they are purchasing.

 Response 3(a). We respectfully
acknowledge your comment. We believe that the Fund’s name is appropriate and is not misleading to retail investors with regard to the nature of the financial instrument they are purchasing in that the registrant is defined as “the
Fund” in the first sentence of the cover page of the Prospectus and is used throughout the Prospectus.

 Comment 3(b). Please
provide disclosure about the type of fund being registered or a statement about fund investment objectives in accord with Item 1.1.b. of Form N-2.

Response 3(b). The disclosure has been revised accordingly.

Comment 3(c). Please provide a brief description of the securities being offered per Item 1.1.c. of Form
N-2. Explain that this is a tender offer fund and discuss repurchase frequency. Also, cross-reference sections of the prospectus that discuss the Fund’s repurchase policies and the attendant risks.

 Response 3(c). The disclosure has been revised accordingly.

Comment 3(d). Please provide the statement required by Item 1.1.d. of Form N-2.

Response 3(d). The disclosure has been revised accordingly.

Comment 3(e). Please state the public offering price in the offering table or provide additional offering table disclosure in accord with
instruction 1 to Item 1.1.g. of Form N-2.

 Response 3(e). Assuming the
Fund has an Initial Closing prior to the effective date of its 1933 Act registration statement, all subsequent closings would be at a public offering price equal to the then current net asset value per share of the applicable class plus the
applicable sales load.

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 Comment 3(f). Although public trading may not occur for two years, consider adding
disclosure required by Item 1.1.i. of Form N-2 concerning the lack of history of public trading of shares of the Fund and closed-end fund discounts. If such disclosure
is not added, explain, supplementally, why such information would not be material to investors purchasing Fund shares now with a view to the development of a secondary market.

Response 3(f). The Nasdaq Private Market currently does not have any secondary trading of
closed-end fund interests, and the development of this secondary market is extremely uncertain. As a result, we do not believe the suggested disclosure is material to investors purchasing Fund shares now. To
the extent such a market does develop, the Fund will update the disclosure as appropriate.

 Comment 3(g). Please add the statement
required by rule 498(b)(1)(vii) under the Securities Act and Item 1.1.l of Form N-2 regarding optional internet availability of investment company shareholder reports, if applicable.

Response 3(g). The disclosure has been revised accordingly.

Comment 3(h). The first sentence of the paragraph under the heading “To All Investors” is redundant of required rule 481
disclosure now included at the top of the cover page. Please delete the redundant language. Also, please delete the subsequent sentences of this paragraph which constitute legalese disclaiming prospectus liability.

Response 3(h). The disclosure has been revised accordingly.

Comment 3(i). Please add Class D Shares to the fourth bullet on the cover page, including notation of the appropriate hurdle
percentage with regard to a total return necessary to recover the sales load.

 Response 3(i). The disclosure has
been revised accordingly.

 Comment 3(j). Please provide disclosure concerning dealer prospectus delivery obligations in accord with
Item 2.3 of Form N-2.

 Response 3(j). The disclosure has been revised
accordingly.

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4.
 Summary of Prospectus

Comment 4(a). The prospectus summary and later sections of the prospectus contain subjective language regarding Fund investment management.
For instance, on page one of the summary the registrant claims that investment will be allocated by one of the most sophisticated institutional investors in private markets. Please redraft to provide a less subjective description of the
Advisers’ qualifications for managing investments in the Fund and also amend other instances throughout the prospectus touting the Advisers’ and co-investors’ investment acumen.

Response 4(a). The disclosure has been revised accordingly.

Comment 4(b). On page two, the registrant outlines the “favorable structure” of the Fund. Please add further disclosure
clarifying that this structure is “favorable” relative to investing directly in private equity funds.

Response 4(b). The disclosure has been revised accordingly.

Comment 4(c). On page two, the registrant describes StepStone’s track record by stating that StepStone has generated
“attractive” risk-adjusted returns. Please provide further disclosure explaining what is meant by “attractive” on page two and also on page four outlining StepStone’s experience.

Response 4(c). The disclosure has been revised accordingly.

Comment 4(d). On page three, the registrant discusses management of the J-Curve and cash flow
dynamics. Please provide plain English disclosure in the section explaining the J-Curve and private markets investing. Further, add corresponding discussion in the principal risks section specifically
detailing the J-Curve and the investing risks it represents as a feature of private markets investing.

Response 4(d). The disclosure has been revised accordingly.

Comment 4(e). On page four, the registrant states that the Advisers and the Fund have obtained an exemptive order that “expands”
the Fund’s ability to co-invest. Please rewrite this disclosure to state that the order “permits” the Fund to co-invest alongside its affiliates in
Private Market Assets; make a corresponding edit to page 39.

 Response 4(e). The disclosure has been revised
accordingly.

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 Comment 4(f). (p. 5) The Fund states that it is not obligated to repurchase any Shares.
The Fund does not have a fundamental policy related to Share repurchases. Please summarize, supplementally, Fund compliance with rule 23c-3 under the 1940 Act governing repurchase offers by closed-end companies.

 Response 4(f). We respectfully acknowledge your
comment. We hereby confirm that the Fund is not an interval fund and will not comply with Rule 23c-3 under the 1940 Act. The Fund’s discretionary quarterly repurchase offers will comply with Rule 13e-4 under the Securities Exchange Act of 1934, as amended.

 Comment 4(g). (p. 5) The Fund states
that the initial per share offering price for Shares was $25. Please confirm that this formulation is correct. It is the staff’s understanding that this filing represents an initial registration statement for the Shares. Accordingly, the
initial per share offering price should be $25 in the future at the time of the initial public offering.

 Response
4(g). Assuming the Fund has an Initial Closing prior to the effective date of its 1933 Act registration statement, all subsequent closings would be at a public offering price equal to the then current net asset value per share of the applicable
class plus the applicable sales load. The relevant purchase price disclosure has been revised accordingly.

 Comment 4(h). (p. 6) Please
provide the breakdown of any fee splitting between the financial advisor and distributor for Class S and Class D Shares.

Response 4(h). We respectfully acknowledge your comment. We note that there is no fee splitting between the financial
advisor and distributor. The disclosure has been revised accordingly.

 Comment 4(i). (p. 9) The Fund describes Nasdaq Private Market as
operating an online platform designed to conduct auctions for unregistered securities. Please clarify what is meant by “unregistered securities” given that the Fund’s shares will be registered under the 33 Act. Also, make
corresponding changes with respect to description of the auction process on page 60.

 Response 4(i). The
relevant disclosure has been revised to change the references to “unlisted securities.”

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 Comment 4(j). On page ten, the registrant summarizes “material risks” involved
in an investment in the Fund. Please redraft this section label using the appropriate 40 Act terms for such risks: “principal risks.”

Response 4(j). The disclosure has been revised accordingly.

5.
 Summary of Fees and Expenses

Comment 5(a). Please change the fee table category labels for the fees being charged in order to provide more clarity as follows. Use the
terms “Shareholder Fees” instead of Transaction Fees, “Annual Fund Operating Expenses” instead of Annual Fund Expenses, and “Total Annual Fund Operating Expenses” instead of Total Annual Net Expenses.

Response 5(a). The disclosure has been revised accordingly.

Comment 5(b). The registrant opens this section by stating that the following fees and expenses are estimates based upon net assets of
$400,000,000; however, on page one of the summary the registrant states it is initially registering $500,000,000. Please reconcile.

Response 5(b). The disclosure that introduces the fee table assumes the Fund will have $400 million in
subscriptions during its first year of operations. The Fund will be continuously offered and is registering $500 million of shares in connection with its continuous offering. As such, we believe the disclosure is appropriate.

Comment 5(c). On page 7 of the prospectus summary, the registrant states that the Fund will pay for certain recurring expenses, including
administrative costs and organizational and offering costs. Please add footnote disclosure to the fee table explaining these costs. Also, expand on this disclosure later in the prospectus in the Fund Expenses section.

Response 5(c). The disclosure has been revised accordingly.

Comment 5(d). The fee and expenses table indicates that “Other Expenses” will be 1.07% of net assets. Please reconcile this
amount with the expense reimbursement agreement which should cap such “Other Expenses” at 1.00%.

 Response
5(d). We respectfully acknowledge your comment. The “Other Expenses” line item includes certain costs related to the Fund’s credit facility, which are not covered under the expense reimbursement agreement.

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 Comment 5(e). The expense examples on page 13 assumes a 2% Early Repurchase Fee. Given
that this fee applies to periods of less than one year, this fee should not be shown in the expense examples. Nevertheless, please provide text immediately after the expense examples explaining that if an investor’s Shares are repurchased in
the first year such Shares would be subject to the 2.00% Early Repurchase Fee. Also include in such text the 1-year expense figures for such Shares under the assumptions of the example for all four classes.

 Response 5(e). The disclosure has been revised accordingly.

Comment 5(f). The expense example assumes continuation of the expense cap beyond year one. Given the expense agreement is only for one year
and must be renewed annually, please revise the examples so that the expense waiver is not reflected beyond year one.

Response 5(f). The examples have been so revised.

Comment 5(g). Please reorder the expense table line items so that other expenses is the last line item before Total Fund Operating
Expenses.

 Response 5(g). The expense table line items have been reordered.

6.
 Use of Proceeds

Comment 6(a). Please disclose how long it is expected to take to fully invest net proceeds in accordance with the registrant’s
investment objectives and policies, the reasons for any anticipated lengthy delay in investing the net proceeds, and the