UNITED STATES
               SECURITIES AND EXCHANGE COMMISSION
                     Washington, D.C. 20549

                           FORM 10-Q

[X]   Quarterly  report pursuant to Section 13 or  15(d)  of  the
Securities Exchange Act of 1934
For the quarterly period ended September 30, 1998 or

[  ]   Transition report pursuant to Section 13 or 15(d)  of  the
Securities Exchange Act of 1934
For the transition period from ________________to_____________

Commission File Number 0-13299


                DEAN WITTER CORNERSTONE FUND III
    (Exact name of registrant as specified in its charter)


                New   York                             13-3190919
(State or other jurisdiction of              (I.R.S. Employer
incorporation or organization)               Identification No.)


c/o Demeter Management Corporation
Two  World  Trade  Center, 62 Fl.,  New  York,  NY          10048
(Address of principal executive offices)           (Zip Code)


Registrant's telephone number, including area code (212) 392-5454

(Former  name, former address, and former fiscal year, if changed
since last report)


Indicate  by check-mark whether the registrant (1) has filed  all
reports  required  to be filed by Section  13  or  15(d)  of  the
Securities  Exchange Act of 1934 during the preceding  12  months
(or  for such shorter period that the registrant was required  to
file  such  reports),  and (2) has been subject  to  such  filing
requirements for the past 90 days.

Yes    X       No










<PAGE>
<TABLE>
                                
                DEAN WITTER CORNERSTONE FUND III

             INDEX TO QUARTERLY REPORT ON FORM 10-Q

                       September 30, 1998
<CAPTION>

PART I. FINANCIAL INFORMATION
<S>                                                          <C>
Item 1. Financial Statements

   Statements of Financial Condition
   September 30, 1998 (Unaudited) and December 31, 1997.......2

   Statements of Operations for the Quarters Ended
   September 30, 1998 and 1997 (Unaudited)....................3

   Statements of Operations for the Nine Months Ended
   September 30, 1998 and 1997 (Unaudited)....................4

   Statements of Changes in Partners' Capital for the
   Nine Months Ended September 30, 1998 and 1997 (Unaudited)..5

   Statements of Cash Flows for the Nine Months Ended
   September 30, 1998 and 1997 (Unaudited)....................6

   Notes to Financial Statements (Unaudited)...............7-12

Item 2.  Management's Discussion and Analysis of Financial

Condition and Results of Operations..............13-21

PART II. OTHER INFORMATION

Item 1.  Legal Proceedings...................................22

Item 2.  Changes in Securities and Use of Proceeds...........22

Item 6.  Exhibits and Reports on Form 8-K................... 23





</TABLE>










<PAGE>
<TABLE>
                 PART 1.  FINANCIAL INFORMATION
Item 1.  Financial Statements

                DEAN WITTER CORNERSTONE FUND III
               STATEMENTS OF FINANCIAL CONDITION
<CAPTION>
                                   September 30,   December 31,
                                        1998           1997
                                         $              $
                                    (Unaudited)
ASSETS
<S>                               <C>             <C>
Equity in Commodity futures trading accounts:
 Cash                            40,026,415      39,762,715
 Net unrealized gain on open contracts5,041,458   1,938,295
 Net option premiums               (150,813)        (158,765)

 Total Trading Equity            44,917,060      41,542,245

Interest receivable (DWR)           138,562         145,100
Due from DWR                         97,120            94,981

 Total Assets                    45,152,742      41,782,326


LIABILITIES AND PARTNERS' CAPITAL

Liabilities

 Redemptions payable                300,992         429,759
 Accrued management fees            149,521         138,480
 Accrued administrative expenses      147,029        99,713

 Total Liabilities                  597,542         667,952


Partners' Capital

 Limited Partners (12,460.124 and
  13,352.334 Units, respectively)43,229,521      39,970,539
 General Partner (382.103 Units)    1,325,679      1,143,835

 Total Partners' Capital         44,555,200      41,114,374

  Total  Liabilities and Partners' Capital    45,152,742       41
,782,326


NET ASSET VALUE PER UNIT           3,469.43          2,993.52

<FN>

          The accompanying notes are an integral part
                 of these financial statements.
</TABLE>

<PAGE>
<TABLE>
                DEAN WITTER CORNERSTONE FUND III
                    STATEMENTS OF OPERATIONS
                           (Unaudited)

<CAPTION>




                              For the Quarters Ended September 30,

                                       1998            1997
                                        $            $
REVENUES
<S>                         <C>              <C>
 Trading profit (loss):
    Realized                       1,195,020 1,591,335
    Net change in unrealized       3,556,398      (511,267)

      Total Trading Results        4,751,418   1,080,068

 Interest Income (DWR)               422,909         456,621

      Total Revenues               5,174,327     1,536,689


EXPENSES

 Brokerage commissions (DWR)       543,426   544,996
 Management fees                   434,472     440,963
 Transaction fees and costs         57,477    54,218
 Administrative expenses            20,852        19,651

      Total Expenses             1,056,227     1,059,828

NET INCOME                       4,118,100        476,861


NET INCOME ALLOCATION

 Limited Partners                3,997,158   464,881
 General Partner                   120,942    11,980


NET INCOME PER UNIT

 Limited Partners                   316.52   31.36
 General Partner                    316.52     31.36


<FN>
          The accompanying notes are an integral part
                 of these financial statements.

</TABLE>
<PAGE>
<TABLE>
                DEAN WITTER CORNERSTONE FUND III
                    STATEMENTS OF OPERATIONS
                           (Unaudited)


<CAPTION>



                             For the Nine Months Ended September 30,

                                       1998            1997
                                        $            $
REVENUES
<S>                           <C>            <C>
 Trading profit (loss):
    Realized                       5,018,082     8,294,807
    Net change in unrealized       3,103,163    (1,782,699)

      Total Trading Results        8,121,245  6,512,108

 Interest Income (DWR)             1,280,723     1,356,529

      Total Revenues               9,401,968    7,868,637


EXPENSES

 Brokerage commissions (DWR)       1,636,282 1,729,266
 Management fees                   1,270,563  1,318,572
 Transaction fees and costs          168,130   168,308
 Administrative expenses              53,026          56,005

      Total Expenses               3,128,001     3,272,151

NET INCOME                         6,273,967     4,596,486


NET INCOME ALLOCATION

 Limited Partners                  6,092,123 4,481,552
 General Partner                    181,844       114,934


NET INCOME PER UNIT

 Limited Partners                     475.91    300.80
 General Partner                      475.91    300.80

<FN>

          The accompanying notes are an integral part
                 of these financial statements.
</TABLE>

<PAGE>
<TABLE>
                DEAN WITTER CORNERSTONE FUND III
           STATEMENTS OF CHANGES IN PARTNERS' CAPITAL
     For the Nine Months Ended September 30, 1998 and 1997
                          (Unaudited)


<CAPTION>


                          Units of
                        Partnership Limited   General
                          Interest   Partners Partner    Total



<S>            <C>                         <C>                   <C>
<C>
Partners' Capital
 December 31, 1996   15,479.706            $40,997,752           $1,037,606
$42,035,358

Offering of Units         1.841              5,000       -            5,000

Net Income                 -               4,481,552             114,934
4,596,486

Redemptions           (1,429.733)            (4,252,253)                    -
(4,252,253)

Partners' Capital
 September 30, 1997   14,051.814            $41,232,051           $1,152,540
$42,384,591





Partners' Capital
 December 31, 1997   13,734.437            $39,970,539           $1,143,835
$41,114,374

Offering of Units         5.184             15,998     -              15,998

Net Income               -                 6,092,123             181,844
6,273,967

Redemptions             (897.394)          (2,849,139)                    -
(2,849,139)

Partners' Capital
 September 30, 1998    12,842.227          $43,229,521           $1,325,679
$44,555,200



<FN>



           The accompanying notes are an integral part
                 of these financial statements.
</TABLE>


<PAGE>
<TABLE>

                DEAN WITTER CORNERSTONE FUND III
                    STATEMENTS OF CASH FLOWS
                           (Unaudited)


<CAPTION>



                             For the Nine Months Ended September 30,

                                       1998            1997
                                        $            $
CASH FLOWS FROM OPERATING ACTIVITIES
<S>                           <C>                        <C>
Net   income                           6,273,967                4
,596,486
Noncash item included in net income:
      Net  change  in  unrealized       (3,103,163)             1
,782,699

 (Increase) decrease in operating assets:
    Net option premiums               (7,952)            6,872
    Interest receivable (DWR)         6,538              (6,854)
    Due from DWR                      (2,139)            65,407


 Increase (decrease) in operating liabilities:
    Accrued management fees           11,041             498
    Acccrued administrative expenses   47,316            8,975
    Accrued brokerage commissions (DWR) -                (33,408)
       Accrued    transaction    fees    and    costs           -
(5,471)

Net    cash    provided   by   operating   activities   3,225,608
6,415,204


CASH FLOWS FROM FINANCING ACTIVITIES

 Offering of units                   15,998              5,000
   Decrease  in  redemptions  payable     (128,767)             (
199,895)
   Redemptions  of  units              (2,849,139)              (
4,252,253)

Net  cash  used  for  financing  activities   (2,961,908)       (
4,447,148)


Net   increase  in  cash                 263,700                1
,968,056

Balance  at  beginning  of  period    39,762,715                4
0,587,011

Balance  at  end  of  period          40,026,415                4
2,555,067

<FN>

           The accompanying notes are an integral part
                 of these financial statements.
</TABLE>
<PAGE>

                DEAN WITTER CORNERSTONE FUND III

                  NOTES TO FINANCIAL STATEMENTS

                           (UNAUDITED)

                                

The  financial statements include, in the opinion of  management,

all  adjustments necessary for a fair presentation of the results

of  operations and financial condition of Dean Witter Cornerstone

Fund  III  (the  "Partnership").  The  financial  statements  and

condensed  notes  herein should be read in conjunction  with  the

Partnership's December 31, 1997 Annual Report on Form 10-K.

1. Organization

Dean  Witter  Cornerstone  Fund  III  is  a  limited  partnership

organized  to  engage  in the speculative  trading  of  commodity

futures  contracts  and forward contracts on  foreign  currencies

(collectively, "futures interests").  The Partnership is  one  of

the  Dean  Witter  Cornerstone Funds, comprised  of  Dean  Witter

Cornerstone Fund II, the Partnership, and Dean Witter Cornerstone

Fund  IV.   The general partner is Demeter Management Corporation

("Demeter").   The non-clearing commodity broker is  Dean  Witter

Reynolds  Inc.  ("DWR"), an affiliate of Demeter.   The  clearing

commodity   broker  is  Carr  Futures  Inc.  ("Carr"),  providing

clearing and execution services. Both Demeter and DWR are wholly-

owned  subsidiaries of Morgan Stanley Dean Witter & Co. ("MSDW").

The  trading  advisors  who make all trading  decisions  for  the

Partnership   are   Abraham  Trading   Co.,   Welton   Investment

Corporation  and Sunrise Capital Management, Inc.  (the  "Trading

Advisors").





<PAGE>

                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONTINUED)



2. Related Party Transactions

The Partnership's cash is on deposit with DWR and Carr in futures

interest trading accounts to meet margin requirements as  needed.

DWR  pays  interest on these funds based on current 13-week  U.S.

Treasury  bill  rates.   Brokerage  expenses  incurred   by   the

Partnership are paid to DWR.


3. Financial Instruments

The Partnership trades futures, options, and forward contracts in

interest   rates,  stock  indices,  commodities  and  currencies.

Futures and forwards represent contracts for delayed delivery  of

an  instrument at a specified date and price.  Risk  arises  from

changes  in  the  value  of  these contracts  and  the  potential

inability  of  counterparties to perform under the terms  of  the

contracts.   There  are numerous factors which may  significantly

influence the market value of these contracts, including interest

rate  volatility.  At September 30, 1998 and December  31,  1997,

open contracts were:

                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
<PAGE>
                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONTINUED)


                               Contract or Notional Amount
                            September 30, 1998 December 31, 1997
                                      $              $
Exchange-Traded Contracts
 Financial Futures:
   Commitments to Purchase       170,529,000        50,242,000
   Commitments to Sell             5,520,000        21,172,000
     Options   Written                  13,334,000              -
Commodity Futures:
   Commitments to Purchase         6,276,000         8,055,000
   Commitments to Sell            13,801,000        31,622,000
   Options Written                 6,835,000            -
 Foreign Futures:
   Commitments to Purchase       224,483,000        50,870,000
   Commitments to Sell            12,223,000        42,064,000
   Options Written                     5,000            -
Off-Exchange-Traded
 Forward Currency Contracts
   Commitments to Purchase        35,575,000        27,863,000
   Commitments to Sell            11,845,000        41,794,000


A  portion of the amounts indicated as off-balance-sheet risk  in

forward   currency   contracts  is  due  to  offsetting   forward

commitments  to purchase and sell the same currency on  the  same

date   in   the   future.   These  commitments  are  economically

offsetting,  but are not offset in the forward market  until  the

settlement date.

                                
The  net  unrealized gain on open contracts  are  reported  as  a

component  of  "Equity in Commodity futures trading accounts"  on

the  Statements of Financial Condition and totaled $5,041,458 and

$1,938,295  at  September  30,  1998  and  December   31,   1997,

respectively.

                                

                                
                                
                                
<PAGE>
                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONTINUED)




Of  the  $5,041,458  net unrealized gain  on  open  contracts  at

September 30, 1998, $4,489,038 related to exchange-traded futures

contracts  and  $552,420  related to off-exchange-traded  forward

currency contracts.



Of  the  $1,938,295  net unrealized gain  on  open  contracts  at

December 31, 1997, $2,168,497 related to exchange-traded  futures

contracts  and $(230,202) related to off-exchange-traded  forward

currency contracts.



Exchange-traded  futures contracts held  by  the  Partnership  at

September 30, 1998 and December 31, 1997 mature through June 1999

and   June   1998,  respectively.   Off-exchange-traded   forward

currency contracts held by the Partnership at September 30,  1998

and  December  31, 1997 mature through December  1998  and  March

1998, respectively.



The   contract   amounts  in  the  above  table   represent   the

Partnership's  extent  of involvement in a  particular  class  of

financial  instrument, but not the credit  risk  associated  with

counterparty  non-performance.  The credit risk  associated  with

these  instruments  is limited to the amounts  reflected  in  the

Partnership's Statements of Financial Condition.





<PAGE>
                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONTINUED)




The Partnership also has credit risk because DWR and Carr act  as

the  futures  commission  merchants or the  counterparties,  with

respect  to  most  of the Partnership's assets.   Exchange-traded

futures  contracts  are marked to market on a daily  basis,  with

variations  in value settled on a daily basis.  Each of  DWR  and

Carr,  as  a  futures commission merchant for  the  Partnership's

exchange-traded futures and futures styled options contracts, are

required,  pursuant  to  regulations  of  the  Commodity  Futures

Trading  Commission ("CFTC"), to segregate from their own assets,

and  for the sole benefit of their commodity customers, all funds

held  by them with respect to exchange-traded futures and futures

styled  options contracts, including an amount equal to  the  net

unrealized  gain on all open futures and futures  styled  options

contracts, which funds, in the aggregate, totaled $44,515,453 and

$41,931,212  at  September  30,  1998  and  December  31,   1997,

respectively.  With  respect  to the Partnership's  off-exchange-

traded forward currency contracts, there are no daily settlements

of  variations  in  value nor is there any  requirement  that  an

amount equal to the net unrealized gain on open forward contracts

be segregated.  With respect to those off-exchange traded forward

currency contracts, the Partnership is at risk to the ability  of

Carr,  the  sole counterparty on all such contracts, to  perform.

Carr's  parent, Credit Agricole Indosuez, has guaranteed  to  the

Partnership  payment  of  the  net  liquidating  value   of   the

transactions in the



<PAGE>

                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONCLUDED)




Partnership's  account  with  Carr  (including  foreign  currency

contracts).



For  the nine months ended September 30, 1998 and the year  ended

December   31,   1997,  the  average  fair  value  of   financial

instruments held for trading purposes was as follows:




                                       September 30, 1998
                                       Assets        Liabilities
                                         $               $

Exchange-Traded Contracts:
  Financial Futures                 94,147,000       18,544,000
  Options on Financial Futures           -           33,597,000
  Commodity Futures                  5,493,000       24,922,000
  Options on Commodity Futures           -            1,555,000
  Foreign Futures                  100,022,000       24,662,000
  Options on Foreign Futures             -                1,000
Off-Exchange-Traded Forward
 Currency Contracts                 45,041,000       46,002,000


                                        December 31, 1997
                                       Assets        Liabilities
                                         $               $

Exchange-Traded Contracts:
  Financial Futures                 82,881,000       46,462,000
  Options on Financial Futures         698,000       64,639,000
  Commodity Futures                 26,095,000       21,377,000
  Options on Commodity Futures       1,117,000        4,712,000
  Foreign Futures                   44,764,000       26,219,000
  Options on Foreign Futures         7,229,000            -
Off-Exchange-Traded Forward
 Currency Contracts                 12,599,000       13,558,000

                                
                                
                                
                                
<PAGE>

Item   2.  MANAGEMENT'S  DISCUSSION  AND  ANALYSIS  OF  FINANCIAL
CONDITION AND RESULTS OF OPERATIONS


Liquidity - Assets of the Partnership are deposited with  DWR  as

non-clearing  broker  and  Carr as clearing  broker  in  separate

futures  interest trading accounts established for  each  Trading

Advisor  and are used by the Partnership as margin to  engage  in

futures  interest trading.  Such assets are held in  either  non-

interest bearing bank accounts or in securities approved  by  the

CFTC  for investment of customer funds.  The Partnership's assets

held  by  DWR  and  Carr  may be used as margin  solely  for  the

Partnership's trading.  Since the Partnership's sole  purpose  is

to   trade  in  futures  interests,  it  is  expected  that   the

Partnership  will continue to own such liquid assets  for  margin

purposes.



The  Partnership's investment in futures interests may, from time

to time, be illiquid.  Most United States futures exchanges limit

fluctuations in certain futures interest prices during  a  single

day  by  regulations  referred to as  "daily  price  fluctuations

limits" or "daily limits."  Pursuant to such regulations,  during

a  single trading day no trades may be executed at prices  beyond

the  daily limit.  If the price for a particular futures interest

has increased or decreased by an amount equal to the daily limit,

positions  in  such  futures interest can neither  be  taken  nor

liquidated  unless  traders are willing to effect  trades  at  or

within  the  limit.   Futures interests prices have  occasionally

moved the daily limit for several consecutive days with little or

no trading.  Such market conditions could prevent the Partnership

                                

<PAGE>

from  promptly  liquidating its futures interests and  result  in

restrictions on redemptions.



There  is  no limitation on daily price moves in trading  forward

contracts  on  foreign  currency.  The  markets  for  some  world

currencies  have low trading volume and are illiquid,  which  may

prevent  the  Partnership from trading in potentially  profitable

markets  or  prevent  the Partnership from  promptly  liquidating

unfavorable  positions  in  such markets  and  subjecting  it  to

substantial  losses.   Either of these  market  conditions  could

result in restrictions on redemptions.


Capital  Resources  The Partnership does not have,  nor  does  it

expect  to  have,  any  capital assets.  Future  redemptions  and

exchanges  of Units of Limited Partnership Interest  will  affect

the amount of funds available for investment in futures interests

in  subsequent periods.  Since they are at the discretion of  the

Limited  Partners, it is not possible to estimate the amount  and

therefore, the impact of future redemptions and exchanges.



Results of Operations

For the Quarter and Nine Months Ended September 30, 1998

For  the  quarter  ended  September  30,  1998,  the  Partnership

recorded  total  trading revenues including  interest  income  of

$5,174,327  and posted an increase in Net Asset Value  per  Unit.

The  most  significant gains were recorded in the global interest

rate  futures  markets  during August  and  September  from  long

positions in U.S. and European bond futures as prices in these

<PAGE>

markets  trended higher.  Most global bond prices rallied  higher

during  the last two months of the quarter as investors continued

to  flock  to  these  perceived "safe havens"  due  to  worldwide

economic  uncertainty and the subsequent volatility.   Additional

gains were recorded in this market complex as long Japanese  bond

futures  positions profited from the upward trend in prices.   In

the  agricultural  markets,  profits  were  recorded  from  short

positions  in the livestock and corn futures as prices  in  these

markets  decreased  during  July and  August  due  to  increasing

supplies  and  declining demand.  A portion of  these  gains  was

offset by losses recorded in global stock index futures from long

S&P  500 Index futures positions as domestic stock prices plunged

during  late  July  and throughout August after  reaching  record

levels early in the quarter.  Additional losses were recorded  in

the  metals  markets  during July from short  positions  in  base

metals futures as prices moved higher early in the month.   As  a

result of this move higher, long positions in these markets  were

established only to result in additional losses in late  July  as

prices regained their previous downward momentum.  Smaller losses

were  recorded in energy futures trading during September.  Total

expenses  for  the  three months ended September  30,  1998  were

$1,056,227, resulting in net income of $4,118,100.  The value  of

an individual Unit in the Partnership increased from $3,152.91 at

June 30, 1998 to $3,469.43 at September 30, 1998.



For  the  nine  months  ended September 30, 1998,  the  Partnership

recorded  total  trading  revenues  including  interest  income  of

$9,401,968 and posted an increase in Net Asset Value per Unit.  The

<PAGE>

most  significant  profits  were recorded  from  long  global  bond

futures  positions,  particularly U.S.  and  German  bond  futures,

during  the third quarter as a result of a strong upward  trend  in

prices  during August and September.  Most global bond prices  were

pushed  significantly higher during this period as investors sought

a  "safe  haven"  in  lieu of the worldwide  economic  instability,

particularly  in emerging markets.  Smaller profits  were  recorded

from  long  positions in Japanese bond futures as  prices  in  this

market also trended higher.  In global stock index futures, profits

were  recorded  from  long U.S. and European  stock  index  futures

positions as prices in these markets trended consistently higher to

record  highs  throughout the first six months of the  year  before

reversing  sharply  lower  during  late  July  and  early   August.

Additional  gains  were recorded in livestock  futures  from  short

cattle  and  hog futures as prices declined during the  second  and

third  quarters.  Gains were recorded in energies from short  crude

oil  futures  positions as oil prices declined during  January  and

February  on news of easing tensions in the Middle East, and  again

during  May,  June  and  July on reports  of  increasing  supplies.

Smaller  gains were recorded from short positions in sugar  futures

as sugar prices trended lower between January and April.  A portion

of  these gains was offset by losses recorded in the metals markets

from  short  gold futures positions as gold prices reversed  higher

during  January and September.  Smaller losses were  recorded  from

long  silver  futures during March as silver prices reversed  lower

after  trending steadily higher during January and early  February.

In currencies, losses were recorded from transactions involving the

British pound, as its

                                

<PAGE>

value  moved  in  a trendless pattern relative to the  U.S.  dollar

during  the first nine months of the year.  Total expenses for  the

nine months ended September 30, 1998 were $3,128,001, resulting  in

net  income of $6,273,967.  The value of an individual Unit in  the

Partnership  increased  from $2,993.52  at  December  31,  1997  to

$3,469.43 at September 30, 1998.

                                

For the Quarter and Nine Months Ended September 30, 1997

For  the  quarter  ended  September  30,  1997,  the  Partnership

recorded  total  trading revenues including  interest  income  of

$1,536,689  and posted an increase in Net Asset Value  per  Unit.

The most significant gains were recorded in the financial futures

markets,  particularly in Australian, Japanese and European  bond

futures,  due  to an upward move in global interest rate  futures

prices  during  July and September.  Smaller gains were  recorded

from  long  U.S. and European stock index futures  as  prices  in

these markets also increased during July.  In currencies, profits

were recorded during July from short positions in the German mark

as  the  value  of  the U.S. dollar increased  versus  the  mark.

Smaller  gains  were  recorded in the energy  markets  from  long

natural gas futures positions as prices moved dramatically higher

during  August  and  September.  A portion of  the  Partnership's

overall gains for the quarter was offset by losses recorded  from

trendless  price  movement in agriculturals and soft  commodities

throughout  a  majority of the quarter.  Total expenses  for  the

three  months ended September 30, 1997 were $1,059,828, resulting

in  net  income of $476,861.  The value of an individual Unit  in

the Partnership

                                

<PAGE>

increased  from  $2,984.95  at June  30,  1997  to  $3,016.31  at

September 30, 1997.



For  the  nine  months ended September 30, 1997, the  Partnership

recorded  total  trading revenues including  interest  income  of

$7,868,637  and posted an increase in Net Asset Value  per  Unit.

The  most significant gains were recorded in the soft commodities

markets  from  long  coffee futures positions  as  coffee  prices

trended higher during January and February and again during April

and May.  Gains were also recorded in the currency markets as the

value  of  the  U.S. dollar strengthened relative to  most  world

currencies during the first and third quarters of the  year.   In

financial  futures trading, gains were recorded from long  global

stock  index  futures positions as global equity  prices  trended

higher  between May and July.  Smaller gains were recorded during

the  third  quarter from a bullish trend in global interest  rate

futures  prices.  Smaller profits were experienced in the  metals

markets  during January, February and July from long zinc futures

positions  as prices in this market moved higher.  A  portion  of

the  Partnership's  gains  was offset  by  losses  recorded  from

trading  energy  futures  as oil and  gas  prices  moved  without

consistent  direction for a majority of the year.  One  exception

in  the  energy  complex  was natural gas futures  prices,  which

increased  steadily during the third quarter, thus  resulting  in

profits  from  long  positions.   In  the  agricultural  markets,

smaller  losses  were experienced from trading livestock  futures

earlier  in  the year.  Total expenses for the nine months  ended

September 30, 1997 were $3,272,151, resulting in net income of

<PAGE>

$4,596,486.   The value of an individual Unit in the  Partnership

increased  from  $2,715.51 at December 31, 1996 to  $3,016.31  at

September 30, 1997.



Year  2000 Problem - Commodity pools, like financial and business

organizations  and individuals around the world,  depend  on  the

smooth functioning of computer systems.  Many computer systems in

use  today cannot recognize the computer code for the year  2000,

but revert to 1900 or some other date.  This is commonly known as

the  "Year  2000  Problem."  The Partnership could  be  adversely

affected  if computer systems used by it or any third party  with

whom  it has a material relationship do not properly process  and

calculate date-related information and data concerning  dates  on

or  after  January 1, 2000.  Such a failure could have a negative

impact  on  the handling or determination of futures  trades  and

prices and the services provided to the Partnership.



MSDW  began its planning in response to the Year 2000 Problem  in

1995  and currently has several hundred employees working on such

response.  It has developed its own Year 2000 compliance plan  to

deal  with the problem and had the plan approved by the company's

executive   management,  Board  of  Directors   and   Information

Technology  Department.   Demeter is coordinating  with  MSDW  in

taking steps that both believe are reasonably designed to address

the  Year 2000 Problem with respect to Demeter's computer systems

that  relate  to  the  Partnership.  This includes  hardware  and

software upgrades, systems consulting and computer maintenance.

                                

<PAGE>

Beyond  the  challenge  facing  internal  computer  systems,  the

systems  failure  of  any  of the third  parties  with  whom  the

Partnership  has a material relationship - the futures  exchanges

and  clearing organizations through which it trades, Carr, or the

Trading  Advisors - could result in a material financial risk  to

the  Partnership.   Regarding  the futures  exchanges,  all  U.S.

futures  exchanges will be subject to the monitoring of the  CFTC

for  their  Year 2000 preparedness and the major foreign  futures

exchanges are also expected to be subject to market-wide  testing

of  their Year 2000 compliance during 1999.  With respect to Carr

and  the  Trading  Advisors, Demeter  intends  to  monitor  their

progress throughout 1999 in their Year 2000 compliance and, where

applicable,  to  test its external interface with  Carr  and  the

Trading Advisors.



Finally, MSDW has begun developing various "contingency plans" in

the  event  that  the  systems of such third  parties  fail,  and

Demeter  intends  to  consult closely with MSDW  in  implementing

those   plans.   MSDW  has  also  recently  reported   that   its

development of such contingency plans is proceeding on  schedule.

Despite the best efforts of both Demeter and MSDW, however, there

can  be  no assurance that the above steps will be sufficient  to

avoid  any  adverse  impact  to  the  Partnership,  whether  from

failures  in  their own computer systems or those  of  Carr,  the

Trading Advisors or any other third party.



Risks  Associated  with  the Euro - On January  1,  1999,  eleven

countries in the European Union intend to establish fixed

<PAGE>

conversion  rates  on  their existing  sovereign  currencies  and

convert to a common single currency (the "euro").  During a three-

year  transition  period, the existing sovereign currencies  will

continue  to exist but only as a fixed denomination of the  euro.

Conversion  to  the euro will prevent the Trading  Advisors  from

trading  in  certain currencies and thereby limit its ability  to

take  advantage  of  potential market  opportunities  that  might

otherwise have existed had separate currencies been available  to

trade,  and  could  result  in  losses  with  respect  to   those

positions.





































<PAGE>

                  PART II.   OTHER INFORMATION



Item 1.  LEGAL PROCEEDINGS

Previously filed.  See Form 10-Q for the quarter ended March  31,

1998.



Item 2.  CHANGES IN SECURITIES AND USE OF PROCEEDS

Dean  Witter  Cornerstone  Fund I ("Cornerstone  I"),  Dean  Witter

Cornerstone   Fund  II  ("Cornerstone  II"),  and  the  Partnership

collectively  registered  250,000  Units  of  Limited   Partnership

Interest ("Units") pursuant to a Registration Statement on Form  S-

1,  which  became  effective  on May 31,  1984  (the  "Registration

Statement")  (SEC  File  Numbers 2-88587; 88587-01;  88587-02).  As

contemplated  in  the Registration Statement, an  additional  fund,

Dean Witter Cornerstone Fund IV ("Cornerstone IV" and, collectively

with  Cornerstone  I,  Cornerstone  II  and  the  Partnership,  the

"Cornerstone  Funds"),  was registered pursuant  to  Post-Effective

Amendment  No.  5  to  the  Registration  Statement,  which  became

effective  on  February 6, 1987. The managing underwriter  for  the

Cornerstone Funds is DWR.


The  offering for the Partnership originally commenced on  May  31,

1984  and  currently continues with 74,405.186 Units  sold  through

September  30,  1998.  Through September 30, 1998, the  Cornerstone

Funds   have  sold  an  aggregate  of  235,414.617  Units   leaving

14,585.383  Units  remaining available for sale as  of  October  1,

1998.



The aggregate price of Units sold through September 30, 1998 with

respect to the Partnership is $137,132,762.

<PAGE>

                                

Item 6. - EXHIBITS AND REPORTS ON FORM 8-K

Reports  on Form 8-K - No reports have been filed for the quarter

ended September 30, 1998.

















































<PAGE>





                           SIGNATURE



Pursuant  to the requirements of the Securities Exchange  Act  of
1934, the Registrant has duly caused this report to be signed  on
its behalf by the undersigned, thereunto duly authorized.




                               Dean Witter Cornerstone Fund III
                                        (Registrant)

                               By: Demeter Management Corporation
                                       (General Partner)

November 13, 1998              By: /s/ Lewis A. Raibley, III
                                       Lewis A. Raibley, III
                                       Chief Financial Officer




The  General  Partner which signed the above is  the  only  party
authorized  to  act  for the Registrant.  The Registrant  has  no
principal   executive  officer,  principal   financial   officer,
controller, or principal accounting officer and has no  Board  of
Directors.