SMITH BARNEY DIVERSIFIED FUTURES FUND L P II
497, 1997-06-23
SECURITY & COMMODITY BROKERS, DEALERS, EXCHANGES & SERVICES
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                      Smith Barney Futures Management Inc.
                              390 Greenwich Street
                               New York, NY 10013

By EDGAR

Securities and Exchange Commission
450 Fifth Street N.W.
Washington, D.C. 20549

RE:  Smith Barney Diversified Futures Fund L.P. II
     Supplement to Registration Statement on Form S-1
     File No. 333-3538

Ladies and Gentlemen:

On Behalf of Smith Barney Diversified Futures Fund L.P. II (the "Partnership") I
am  transmitting  herewith  for  filing,  pursuant  to  Rule  424 (b) (3) of the
Securities  Act of 1933,  as amended,  a Supplement  dated May 31, 1997 to the
Partnership's final prospectus dated May 31, 1996.

Should you have any questions, please telephone me at 723-5424.

Very truly yours,

/s/ Daniel A. Dantuono
    Daniel A. Dantuono
    Chief Financial Officer and
    Director

Enclosures
                                       1
<PAGE>
                                 Smith Barney
                       Diversified Futures Fund L.P. II
                                   May 1997



The net asset value of the Smith  Barney  Diversified  Futures  Fund L.P. II was
$1,109.52  at the end of May,  down  0.3%  from the  close of  April.  Continued
volatility and difficult trading  conditions in financial futures markets led to
overall negative results for the month.

Losses  incurred in the  financial  futures  markets were mainly due to volatile
trading conditions in  global  currencies.  Advisors'  positions in the Japanese
yen produced the largest  losses as sentiment for the currency  shifted  sharply
during  the  month.   Global  interest  rate  markets  were  equally  unsettled,
reflecting  U.S.  interest  rate  concerns  and doubts about  monetary  union in
Europe. Small gains in stock indices,  generated from advisors' positions in the
Japanese nikkei, failed to offset losses in the global bond markets.

In the energy markets,  positions in crude oil resulted in losses. In the metals
markets,  increased  industrial  demand  for  copper  pressured  prices  upward,
resulting in gains for the advisors' long positions.

In the softs markets,  coffee prices  continued an upward trend,  exceeding $3 a
pound by month end as labor  unrest and heavy rains in major producing countries
threatened to reduce already tight inventories.  Advisors continued to gain from
these positions.

The powerful  trends across  several  market sectors that gave the advisors such
strong  performance  in the last  quarter of 1996 and early 1997  appear to have
ended.  The recently  volatile but  non-trending  markets are a normal part of a
concluding market cycle and often set the stage for impending new trends.


Smith Barney Futures Management Inc.

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<PAGE>


                                  Smith Barney
                        Diversified Futures Fund L.P. II
                                Account Statement
                              For the Period May 1,
                              Through May 31, 1997


                                                                Percent
                                                              of Average
                                                              Net Assets
                                                             -------------

Realized losses from trading           $      (2,260,974)           (2.42)%
Change in unrealized gains/losses
   from trading                                2,542,192             2.72
                                       -----------------     -------------

                                                 281,218             0.30

Less, Brokerage commissions
   and clearing fees ($14,316)                   529,442             0.57
                                       -----------------     -------------


Net realized and unrealized losses              (248,224)           (0.27)
Interest Income                                  312,573             0.33
                                       -----------------     -------------

                                                  64,349             0.06
                                       -----------------     -------------

Less, Expenses:
   Management fees                               217,151             0.23
   Other expenses                                134,149             0.14
                                       -----------------     -------------

                                                 351,300             0.37
                                       -----------------     -------------

Net Loss                                        (286,951)           (0.31)%
                                                             =============

Additions (6,836.0709 L.P. units at
April 30, 1997 net asset value
per unit of $1,112.92)                         7,608,000

Additions (67.3903 G.P. units at
April 30, 1997 net asset value
per unit of $1,112.92)                            75,000

Redemptions (541.1832 units at
May 31, 1997 net asset value
per unit of $1,109.52)                          (600,454)
                                       -----------------

Increase in net assets                         6,795,595

Net Assets, April 30, 1997                    86,363,735

                                       =================
Net Assets, May 31, 1997               $      93,159,330
                                       =================


Net asset value per unit               $        1,109.52
   ($93,159,330/83,963.5257 units)     =================



To the best of the  knowledge  and belief of the  undersigned,  the  information
contained herein is accurate and complete.

By: /s/ Daniel A. Dantuono
        Daniel A. Dantuono
        Chief Financial Officer

Smith Barney
Futures Management Inc.
General Partner, Smith Barney
Diversified Futures Fund L.P. II

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