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APTORUM GROUP LIMITED

17th Floor, Guangdong Investment
Tower

148 Connaught Road Central

Hong Kong

September 5, 2018

VIA EDGAR

Keira Nakada

U.S. Securities and Exchange Commission

Division of Corporation Finance

Office of Consumer Products

100 F Street, N.E.

Mail Stop 4631

Washington, DC 20549

    Re:
    APTORUM GROUP LIMITED

Draft Registration Statement on

Form F-1 Submitted July 13, 2018

CIK No. 0001734005

Dear Ms. Nakada:

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 10, 2018 regarding our Registration Statement on Form F-1 (the “Registration
Statement”) previously submitted on July 13, 2018 in confidentiality. 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.

Please note that new
language we are including in Form F-1 pursuant to your comments, is indicated in this letter in bold, italicized font;
any deletions from the initial Registration Statement are indicated in this letter as strikethrough font.

Draft Registration Statement on Form F-1 Submitted July
13, 2018

Cover Page

    1.
    Please amend your prospectus cover page to state the volume of securities being offered on a minimum and maximum offering basis. Refer to Item 501(b)(2) of Regulation S-K. Additionally, please expand your disclosure to include the date the offering will end, any plans to place funds in escrow, or alternatively, that you have no such plans. Refer to Item 501(b)(8)(iii) of Regulation S-K.

Response: We updated the
cover page of Form F-1 in response to the Staff’s comment. Please note that as of the date of this Form F-1 we have not yet
determined a minimum or maximum offering amount, or the offering period. We plan to have the funds from the offering to be held
in an escrow account and such arrangement has been included in the front cover page of the prospectus with more details (such as
the name of the escrow agent) to be filled in once definitive arrangements have been made.

    1

    2.
    We note your disclosure on page 6 and elsewhere that your Class B ordinary shares are entitled to ten votes per share for any matter submitted for shareholder approval. Please expand your cover page disclosure to briefly discuss your dual-class structure and the relative voting rights of your Class A and Class B ordinary shares.

Response: In response to
the Staff’s comment, we added the following language to the cover page of Form F-1:

“Our
authorized share capital is divided into Class A Ordinary Shares and Class B Ordinary Shares. As of the date of the prospectus,
we have 60,000,000 Class A Ordinary Shares, par value $1.00 each and 40,000,000 Class B Ordinary Shares, par value $1.00 each,
authorized, among which, 5,426,381 Class A Ordinary Shares and 22,437,754 Class B Ordinary Shares are issued and outstanding, respectively.
Holders of Class A Ordinary Shares and Class B Ordinary Shares have the same rights except for voting and conversion rights. In
respect of matters requiring a shareholder vote, each Class A Ordinary Share will be entitled to one vote and each Class B Ordinary
Share will be entitled to ten votes. The Class A Ordinary Shares are not convertible into shares of any other class. The Class
B Ordinary Shares are convertible into Class A Ordinary Shares at any time after issuance at the option of the holder on a one
to one basis.”

    3.
    We note that there is currently no public market for your Class A ordinary shares, that you “plan to apply” to have this class listed on the Nasdaq Global Market, and that the offering is conditioned on the “reasonable expectation” that the shares would qualify for listing. We further note your disclosure that the selling shareholders may not sell “on any trading market” until the shares are approved for listing, but that they may sell in negotiated transactions. Please amend the cover page to indicate that the selling stockholders will sell the shares at a fixed price until the shares are listed on the Nasdaq and thereafter at prevailing market prices or privately negotiated prices.

Response: Pursuant to the
Staff’s comment, we added the requested language on the cover page of Form F-1.

Prospectus Summary

Overview, page 1

    4.
    We note from your disclosure that you have not yet conducted any clinical trials. Terms such as “award-winning” and “first-in-class” suggest that the product candidates are effective and likely to be approved. Please delete these references throughout your registration statement. If your use of these terms was intended to convey your belief that the products are based on a novel technology or approach and/or is further along in the development process, you may discuss how your technology differs from technology used by competitors and that you are not aware of competing products that are further along in the development process. Statements such as these should be accompanied by cautionary language that the statements are not intended to give any indication that the product candidates have been proven effective or that they will receive regulatory approval. Similarly, please remove the reference to “First-in-Class/Best-in-Class innovations” on page 62 and the statements concerning the poster award and live demonstration prize on page 73.

Response:
Pursuant to the Staff’s comment, we revised our language to remove references to First-in-class/Best-in-class status, as
well as the statements concerning all the awards in the prospectus.

    2

    5.
    We note your disclosure that you may develop formulations of your therapeutic molecules which may qualify as nutraceuticals or some other product category which may be subject to less regulation and provide a faster path to revenue generation. Please expand your disclosure to identify the relevant product candidate(s) and the contingencies to commercializing such product candidate(s) as nutraceuticals. Alternatively, please delete this disclosure.

Response: Pursuant to the
Staff’s comment we decided to delete the disclosure at issue. Although we may develop formulations of our therapeutic molecules
that may qualify as nutraceuticals or some other product category in the future, currently we do not have any definitive plan to
do so.

    6.
    We note your disclosure that you determined to pursue projects in your non-therapeutics segment, such as the AML clinic, to provide some interim revenue. Please balance your disclosure by quantifying your estimated operating expenses and/or identifying the relevant factors to achieving profitability at the clinic.

Response:
Pursuant to the Staff’s comment, we added the bolded language as follows to page 2 of Form F-1:

“Non-Therapeutics
Segment. The non-therapeutics segment (“Aptorum Non-Therapeutics Group”) encompasses two businesses:
(i) the development of surgical robotics and medical devices and (ii) AML Clinic. The development of surgical robotics and medical
devices business is operated through Signate Life Sciences Limited, a subsidiary of Aptorum Therapeutics Limited. The outpatient
clinic is operated through our subsidiary, Aptorum Medical Limited. Effective as of March 2018, we leased office space in Central
Hong Kong as the home to our medical clinic (“AML Clinic”). AML Clinic has commenced operations under the name of Talem
Medical in June 2018. The estimated operating expenses under full capacity operation is to be no more than USD 90,000 per
month. The clinic is expected to reach operating profit in 18 months from the clinic reaching its full operating capacity upon
(i) the successful recruitment of a minimum of six full time physicians (AML Clinic currently has two full time physicians)
and (ii) establishing steady patients flow via brand development. (See “Our Business – Lead Projects and Other
Significant Projects – Other Significant Projects – Aptorum Medical Limited - AML Clinic”)”

    3

Aptorum’s Lead Projects, page 2

    7.
    Please expand the number of columns in the development chart so that it includes all phases of development that must be completed in order to market your products (i.e., Phase 2 and 3). Please make similar revisions to the chart on page 65.

Response: Pursuant to the
Staff’s comment, we expanded the referenced tables to include all phases of development.

    8.
    Please clarify the distinctions between “Target ID & Selection,” “Lead Discovery,” “Lead Optimization” and “IND Enabling” and describe the activities conducted at each of these stages.

Response:
Pursuant to the Staff’s comment, we added the following disclosure to clarify the differences between the referenced phrases
on page 68 of Form F-1:

“Target Identification
& Selection: The target is the naturally existing cellular or modular structure that appears to have an important role in a
particular disease pathway and will be targeted by the drug that will subsequently be developed. Target validation techniques for
different disease areas can be very different but typically include from in vitro and in silico methods through to the use of whole
animal models.

Lead Discovery: Following
“Target Identification & Selection,” compound screening assays are developed as part of the Lead Discovery. ‘Lead’
molecules can mean slightly different things to different researches or companies, but in this Registration Statement, we refer
to Lead Discovery as the process of identifying one or more small molecules with the desired activity against the identified targets.
Leads can be identified through one or more approaches, which can depend on the target and what, if any, previous knowledge exists.

Lead Optimization: In this
stage of the drug discovery process, the aim is to produce a preclinical drug candidate by maintaining the desired and favorable
properties in the lead compounds, while repairing or reducing deficiencies in their structures. For example, to optimize the chemical
structures to improve, among others, efficacy, reduce toxicity, improve metabolism, absorption and pharmacokinetic properties.

IND-Enabling Studies: Includes
all the essential studies such as GLP toxicology studies, pharmacology and efficacy, pharmacokinetics, in vitro metabolism, CMC
studies, and the data of which are used for IND submission.”

    9.
    As you are in the preclinical stage of development, have not completed your preclinical studies and do not intend to submit an IND application until 2020 or 2021, please revise your disclosure to avoid characterizing your chart as a “pipeline” chart.

Response: Pursuant to the
Staff’s comment, we no longer refer to the chart as a “pipeline” chart and we have also revised related disclosure
to reflect the same.

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    10.
    We note your disclosure that “preclinical studies of ALS-1 indicate that it inhibits the replication of influenza virus in vitro with a nanomolar EC50 and protects mice challenged with lethal doses of avian influenza A H5N1.” Please delete this language or place this selected information in its full and proper context by providing the specific details and parameters of the study from which the data was drawn.

Response:
Pursuant to the Staff’s comment we revised the subject disclosure as set forth below on page 2 of
Form F-1. As this is only the summary section, we only provided a brief summary of the related issue.

“ALS-1: Small molecule
intended for the treatment of viral infections caused by Influenza virus A

Professor Richard Kao (Inventor
of ALS-1, Founder and Principal Investigator of Acticule) was the first to identify nucleoprotein (“NP”) as an effective
drug target (Nature Biotechnology. 28:600-605) for the treatment of viral infections caused by Influenza virus A. It is hypothesized
that influenza A NP is an essential protein for the proliferation of the influenza virus. ALS-1 is a novel small drug molecule
which targets viral NP and triggers the aggregation of NP, which prevents the aggregated NP from entering the nucleus. ALS-1 is
designed to target a broad range of NP variants and we believe it is unlikely that ALS-1 will experience the resistance developed
by the viruses against the existing anti-viral therapy. We are exploring ALS-1 as a potential treatment for viral infections caused
by Influenza virus A. It is currently at the Lead Optimization Stage to optimize its drug-like properties.

ALS-1
is a novel small drug molecule which targets viral nucleoprotein (“NP”). It is our hypothesis that influenza A NP is
an essential protein for the proliferation of the influenza virus. ALS-1 targets NP and triggers the aggregation of NP and this
prevents the aggregated NP from entering the nucleus. Our preclinical studies of ALS-1 indicate that it inhibits the replication
of influenza virus in vitro with a nanomolar EC50 and protects mice challenged with lethal doses of avian influenza
A H5N1. Meanwhile, ALS-1 is designed to target a broad range of NP variants and may have the potential to overcome drug resistance.
Professor Richard Kao (Inventor of ALS-1, Founder and Principal Investigator of Acticule) was the first to identify NP as an effective
drug target (Nature Biotechnology. 28:600-605). Since there is no NP inhibitor on the market yet, we believe that ALS-1 has the
potential to be a First-in-Class drug for treating viral infections caused by Influenza virus A.”

    5

    11.
    We note your disclosure on page 3 that “The target site on NP where ALS-1 is acting has been identified and mechanism established. Animal model efficacy has been demonstrated, while chemical structures are being optimized” as well as numerous other statements throughout your registration statement that present your conclusions regarding the safety and efficacy of your product candidates, which are premature and inappropriate for you to make as these determinations are within the sole authority of the U.S. Food and Drug Administration and comparable regulatory bodies. Please revise your disclosure to remove these statements here and throughout your registration statement.

As a non-exhaustive list of examples
only, we note the following statements:

    ●
    “NLS-1 is a drug molecule derived from natural products (green tea) which appears to be effective for the treatment of endometriosis…” on page 4;

    ●
    “In an animal study…oral administration of Pro-EGCG exhibits superior efficacy over other conventional therapeutic agents…” on page 4;

    ●
    “Assuming our research continues to generate positive results…” on page 63;

    ●
    “According to data in our preclinical studies…ALS-1 outperforms oseltamivir (sold under the brand name Tamiflu) in cell-based assays and stops virus replication during the early to late stages of viral infection…” on page 66;

    ●
    “EGCG, a naturally occurring molecule occurring extracted from green tea, appears to be efficacious for the treatment of endometriosis…” on page 68;

    ●
    “The target site has been identified and animal efficacy and safety have been demonstrated…” on page 72; and

    ●
    “We intend to develop SPLS-1 as an alternative treatment for liver cancer, which we believe will offer improved safety and efficacy…” on page 73.

Response: We revised our
disclosure in Form F-1 pursuant to the Staff’s comment. As examples, here is how we revised the examples provided in the
Staff’s comment:

    ●
    “NLS-1 is a drug molecule derived from natural products (green tea) which appears to be effective for the treatment of endometriosis…” on page 4 has been revised as follows;

“NLS-1,
a drug molecule derived from natural products (green tea), is currently under development for the treatment of endometriosis…”
(see Page 5)

    ●
    “In an animal study…oral