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CORRESP
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APTORUM GROUP LIMITED

17th Floor, Guangdong Investment
Tower

148 Connaught Road Central

Hong Kong

September 27, 2019

VIA EDGAR

U.S. Securities and Exchange Commission

Division of Corporation Finance

Office of Healthcare & Insurance

100 F Street, N.E.

Mail Stop 4631

Washington, DC 20549

Re: Aptorum Group Ltd.

Amendment No. 1 to Registration
Statement on Form F-1

Filed August 16, 2019

File No. 333-232510

Dear Sir and Madam:

Aptorum Group Limited
(the “Company,” “Aptorum,” “we,” “us” or “our”)
hereby transmits its response to the letter received from the staff (the “Staff”) of the Securities and Exchange
Commission (the “Commission”), dated August 30, 2019, regarding our Registration Statement on Form F-1 previously
submitted on July 2, 2019 and amended on August 16, 2019 (the “Registration Statement”). For ease of reference,
we have repeated the Commission’s comments in this response and numbered them accordingly. An amended F-1 submitted publicly
accompanying this Response Letter is referred to as Form F-1.

Amendment No. 1 to Registration Statement on Form F-1 filed August
16, 2019

Smart Pharma Token, page 8

 1. We note your response to comment 2 that the SMPT tokens are not being offered or sold to U.S. persons
and that the transaction documents and agreement governing the tokens have expressed restrictions. Please advise us as to the extent
to which you have implemented guidance in SEC Release 33-7516, including, for example, whether the issuer’s website:

 ● is password protected with procedures reasonably designed to ensure that only non-U.S. persons
can obtain access to the token offering;

 ● limits access to the internet offering materials to persons who can demonstrate that they are not
U.S. persons;

 ● includes a prominent disclaimer that clearly provides that the offer is directed only to countries
other than the United States; and/or

 ● provides that the tokens are not being offered in the United
States or to U.S. persons.

    1

Response:

In response to your comment, we reviewed SEC
Release 33-7516. We believe that the measures previously implemented, as discussed in our prior response letter, combined with
additional measures we have since implemented, as described below are reasonably designed
to ensure that the SMPT token offering is not targeted to U.S. persons and to guard against public sales of the SMPT tokens to
U.S. persons.

In particular, on P. 3-4 of our August 16,
2019 response to the Staff’s prior comments (the “First Response Letter”), we noted the following multi-level
approach we implemented to guard
against public sales of the SMPT token to U.S. persons, including but not limited to:

 ● express
                                         restrictions specified in transaction documents and agreements governing SMPT tokens;

 ● restrictive
                                         legend on all SMPT tokens prohibiting SMPT tokens to be offered and sold in the U.S.;

 ● participation
                                         in a Whitelisting Process before purchasing any SMPT token; and

 ● multiple
                                         legal and operation level measures on third party trading platforms.

In response to your current comment, we added
the following to the official website for the SMPT tokens (https://www.smtph.io) (“SMPT Website”):

 a) a prominent pop-up disclaimer on the home page specifying that “The SMPT token is not being
offered to and is not available for sale to citizens, nationals, residents (tax or otherwise), green card holders and/or any company
domiciled in any of the following jurisdictions: (a) the United States of America; (b) Singapore; (c) Hong Kong (except for Professional
Investors); (d) the People’s Republic of China; (e) Samoa, (f) Seychelles, (g) sanctioned countries under the OFAC and (h)
any other jurisdiction which prohibits the sales of security tokens (“Restricted Jurisdiction”). By clicking “accept”,
you understand that this offering is made outside the United States and may not be made to any “U.S. person” as defined
in Rule 902(k) under the Securities Act (a “Non-U.S. Person”) or citizens of other Restricted Jurisdictions”.

 b) a message located at the bottom of the home page stating that the SMPT token is not available for
sale to U.S. persons and reads: “The SMPT token is not registered under the U.S. Securities Act of 1933, as amended (the
“Securities Act”). The SMPT tokens may not be offered for sale, sold or otherwise transferred, either directly or indirectly
in the U.S. or to U.S. persons except in accordance with Regulation S promulgated under the Securities Act, pursuant to an effective
registration statement under the securities act or pursuant to an exemption from registration under the securities act If you are
not sure whether you are eligible to purchase the SMPT token or have any inquiries, please sign up for our Whitelist or email us
at info@smtph.com.”

Based on our understanding of Release No. 33-7516,
specifically Section IV.B, only a U.S. issuer is required to implement password-type procedures
to ensure that only non-U.S. persons can obtain access to the token offering. Aptorum is a foreign private issuer incorporated
in the Cayman Islands and the issuer of the SMPT token, i.e., Smart Pharmaceutical Limited Partnership, is a limited partnership
registered in Seychelles (“SPLP”). The sole general partner of the issuer, i.e., SMTPH Limited, is an international
business company incorporated under the laws of Seychelles. Accordingly, we do not believe it is necessary to implement this measure
for the SMTP token offering to be considered an offshore Internet offering not targeted to U.S. persons.

    2

Release No. 33-7516 sets forth two general
measures where, if implemented, a non-U.S. offeror, would not be generally considered by the SEC to
be an offshore Internet offeror targeting the U.S. (Section III.B):

 ● The
                                         Web site includes a prominent disclaimer making it clear that the offer is directed only
                                         to countries other than the United States; and

 ● The
                                         Web site offeror implements procedures that are reasonably designed to guard against
                                         sales to U.S. persons in the offshore offering. For example, the offeror could ascertain
                                         the purchaser’s residence by obtaining such information as mailing addresses or
                                         telephone numbers (or area code) prior to the sale.

As
described above, we believe both measures have been implemented in light of (i) the prominent disclaimer on the token offering’s
home page and (ii) establishing a whitelisting process designed to guard against sales to U.S. persons in the offshore offering,
as described in the First Response Letter.

With respect to limiting access to the SMPT
token offering materials to persons who can demonstrate that they are not U.S. persons, no one can participate in the offering
or purchase SMPT tokens if s/he refuses or fails to complete the Whitelist Process. Furthermore, only whitelisted private or exchange-based
wallet address(es) are eligible to use the SMPT tokens. We respectfully direct you to Response No. 2 in the First Response Letter,
which discusses the whitelisting process in more detail.

Out of an abundance of caution, we also coded
the following legend into each SMPT token:

THE SMPT TOKENS HAVE NOT
BEEN REGISTERED UNDER THE U.S. SECURITIES ACT OF 1933, AS AMENDED (“SECURITIES ACT”). THE TOKENS WERE ISSUED IN A TRANSACTION
EXEMPT FROM THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT PURSUANT TO REGULATION S PROMULGATED UNDER IT. THE SMPT TOKENS
MAY NOT BE OFFERED OR SOLD IN THE UNITED STATES UNLESS REGISTERED UNDER THE SECURITIES ACT OR AN EXEMPTION FROM REGISTRATION IS
AVAILABLE. TRANSFERS OF THE SMPT TOKENS MAY NOT BE MADE EXCEPT IN ACCORDANCE WITH THE PROVISIONS OF REGULATION S, PURSUANT TO REGISTRATION
UNDER THE SECURITIES ACT, OR PURSUANT TO AN AVAILABLE EXEMPTION FROM REGISTRATION. FURTHER, HEDGING TRANSACTIONS WITH REGARD TO
THE SMPT TOKENS MAY NOT BE CONDUCTED UNLESS IN COMPLIANCE WITH THE SECURITIES ACT.

In light of all of the above, we believe we
have implemented procedures that are reasonably designed to guard against sales to U.S. persons in the SMPT token offering.

 2. Please advise us of the provisions of Regulation S that you are relying upon in offering and selling the SMPT tokens. Please
provide a detailed analysis as to how you meet each element of those provisions.

Response:

Initially, we would like to remind the Staff
that the SMPT tokens are being offered and sold by Smart Pharmaceutical Limited Partnership, a limited partnership registered in
Seychelles (“SPLP”); Aptorum is not offering, selling or issuing the SMPT tokens and Section 5 of the Securities Act
does not apply to SPLP. We tried to convey in our response to Comment 2 in the First Response Letter that we included reference
to Regulation S in the Registration Statement out of an abundance of caution, but we understand that the Staff still has concerns
regarding the availability of such exemption to the SMPT tokens offered by SPLP.

    3

We also want to note that as of the date hereof,
(i) no U.S. person has approached SPLP or its affiliate and expressed interest to purchase the SMPT tokens, (ii) no U.S. person
has signed up to our Whitelist, submitted a Whitelist application, or has otherwise been admitted into our Whitelist, and (iii)
no SMPT token has been transferred to a wallet address associated with a U.S. person.

As intimated in Section III. A. Activities
and Circumstances Requiring Registration of the discussion provided by the Staff’s Corporation Finance division in Accessing
the U.S. Capital Markets – A Brief Overview for Foreign Private Issuers1,
since the issuing entity, SPLP, is not a foreign private issuer and (i) is not trying to conduct the token offering as a public
offering in the U.S., (ii) is not seeking to list the tokens on a national securities exchange or quote the tokens on the OTCBB,
and (iii) does not seem to meet the asset or shareholder base thresholds that otherwise require registration, we respectfully
submit that SPLP does not have to register the token offering under the Securities Act or register the tokens under the Exchange
Act. We found further support for this position through Rule 901 of Regulation S, which states, “For
the purposes only of section 5 of the Act, the terms offer, offer
to sell, sell, sale, and offer to buy shall be deemed to include offers and sales that occur within
the United States and shall be deemed not to include offers and sales that occur outside the United States.”
It is our position that the token offering is occurring outside the United States.

In 1999, the SEC adopted amendments to Regulation
S to stop abuses of such regulation by issuers and others who were using the regulation as a means to distribute securities into
U.S. markets without the protections afforded by the registration process. We support that initiative and neither we nor SPLP is
attempting to distribute the SMPT tokens into the U.S. markets. The final rule release of such amendments cites “that there
should be no presumption that a foreign issuer offering securities overseas is doing so to avoid the registration and disclosure
requirements of the U.S. federal securities laws, even when it has a substantial trading market for its securities in the United
States” as support for not extending the amendments to foreign private issuers, regardless of the relative size of their
U.S. markets to their worldwide trading2.

Although the language in the SEC’s final
rule regarding amendments to Regulation S seems to imply that Regulation S would be equally inapplicable3,
we believe the token offering meets the conditions of Regulation S nevertheless. The availability of the safe harbor provided by
Regulation S is contingent on two general conditions:

 1. The offer and sale must be made in an offshore transaction; and

 2. No “directed selling efforts” may be made by the issuer, a distributor, any of their
respective affiliates or any person acting on their behalf.

We shall address each of these conditions in
turn.

 1. The offer and sale must be made in an offshore transaction

1 https://www.sec.gov/divisions/corpfin/internatl/foreign-private-issuers-overview.shtml

2 https://www.sec.gov/rules/final/33-7505.htm

3 Final Rule: Offshore Offers
and Sales, Release No. 33-7505; 34-39668; File No. S7-8-97) states, “To avoid undue
interference with offshore offering practices of foreign companies, the amendments will apply to the equity securities of U.S.
issuers, but not to the equity securities of foreign issuers.” The token offering is an offshore offering being conducted
by a foreign company and we respectfully believe such sentiment provided by the SEC was included in the final rule for clarification
and equally applies to Regulation S generally.

    4

As set forth in the First Response Letter,
the SMPT tokens are not being offered to a person in the United States. We believe the measures outlined in response to comment
1 above illustrate how the Company guarantees this. Additionally, as further described in response to comment 1, the Whitelist
Process ensures that the buyer of tokens is outside the U.S. or at the very least, provides us a reasonable belief that the buyer
is outside the U.S. Furthermore, the purchase and sale of SMPT tokens takes place on two cryptocurrency exchange platforms, IDAX
and LATOKEN, both of which are located outside the U.S. and the Whitelist Process prevents the SMTP tokens from being sold to a
U.S. person, so a pre-arrangement of that type is extremely unlikely, if not impossible. In fact, we believe that the Whitelist
Process we have in place makes a sale to a U.S. person virtually impossible.

 2. Directed Selling Efforts

We discuss the lack of “directed selling
efforts” in our response to Comment 2 in the First Response Letter, however we have additional reasons to support our determination
that no such efforts are being made.

The information regarding the SMPT token included
in the initial Registration Statement was very limited in nature and was only included because we thought the potential benefits
(i.e. investing and helping to fund a subsidiary’s operations and business, which indirectly impacts our business) were sufficiently
material to warrant disclosure of same to our investors; the disclosure was expanded in response to the Staff’s comments
requesting additional information about the SMPT token.

In addition, while the SMPT tokens was mentioned
in two press releases of the Company dated April 24, 2019 and July 8, 2019, respectively (both of which were filed with the Staff
as attachments to Form 6-K), we did not issue the press releases to market the SMPT tokens to U.S. investors, as the press releases
contain disclaimers declaring that such release is not a solicitation to offer or sell the tokens4
and that same is not permitted in certain jurisdictions.5

We do not think the two press releases qualify
as a publication “with a general circulation in the United States” as such
term is defined in Rule 902 of Regulation S because they were not meant primarily for the U.S. and were intended to reach far beyond
the U.S. markets.

Other than the two press releases mentioned
above, the Company did not conduct any mailings to U.S. investors regarding the SMPT token, did not conduct any seminars about
the SMPT tokens and did not otherwise advertise the SMPT token in the U.S. We respectfully submit that two press releases and disclosure
about the SMPT tokens in the Registration Statements merely containing statements about the existence of the SMPT tokens, that
also include disclaimers about the sala