<PAGE>   1
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                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                                        
                                   FORM 10-Q
                                        
            QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                        SECURITIES EXCHANGE ACT OF 1934
                                        
                  For the quarterly period ended June 30, 1998
                                        
                         Commission file number 1-3677


                            ALCAN ALUMINIUM LIMITED
             (Exact name of registrant as specified in its charter)


<TABLE>
<S>                                       <C>

            CANADA                                    Inapplicable   
(State or Other Jurisdiction of           (I.R.S. Employer Identification No.)
Incorporation or Organization)

</TABLE>
                                        
         1188 SHERBROOKE STREET WEST, MONTREAL, QUEBEC, CANADA H3A 3G2
            (Address of Principal Executive Offices and Postal Code)
                                        
                                 (514) 848-8000
              (Registrant's Telephone Number, including Area Code)

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 _______

At June 30, 1998, the registrant had 227,538,313 shares of common stock
(without nominal or par value) outstanding. 
                                                               
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------

<PAGE>   2
PART I    - FINANCIAL INFORMATION

     In this report, all dollar amounts are stated in U.S. Dollars and all
quantities in metric tons, or tonnes, unless indicated otherwise.  A tonne
is 1,000 kilograms, or 2,204.6 pounds.  The word "Company" refers to Alcan
Aluminium Limited and, where applicable, one or more consolidated
subsidiaries.

Item 1.  Financial Statements

                            ALCAN ALUMINIUM LIMITED

INTERIM CONSOLIDATED STATEMENT OF INCOME
(unaudited)

<TABLE>
<CAPTION>
Periods ended June 30
(in millions of US$,
 except per share amounts)            Second quarter        Six months
                                     ----------------    ----------------
                                      1998      1997      1998      1997  
                                     ------    ------    ------    ------
<S>                                  <C>       <C>       <C>       <C>
REVENUES
 Sales and operating revenues.....   $1,986    $2,011    $3,939    $3,881  
 Other income.....................       19        19        37        47  
                                     ------    ------    ------    ------
                                      2,005     2,030     3,976     3,928  
                                     ------    ------    ------    ------

COSTS AND EXPENSES
 Cost of sales and operating
  expenses........................    1,549     1,552     3,046     3,002  
 Depreciation.....................      113       110       223       217   
 Selling, administrative and
   general expenses...............      113       115       217       218  
 Research and development
   expenses.......................       17        18        34        34  
 Interest.........................       21        26        44        51  
 Other expenses...................        8        19        18        29  
                                     ------    ------    ------    ------
                                      1,821     1,840     3,582     3,551
                                     ------    ------    ------    ------

Income before income taxes
 and other items.................       184       190       394       377  
Income taxes (note 3)............        76        72       154       117  
                                     ------    ------    ------    ------

Income before other items........       108       118       240       260  
Equity income (loss).............       (23)       (1)      (39)        2  
Minority interests...............         1        (1)        2        (3)
                                     ------    ------    ------    ------

NET INCOME.......................    $   86    $  116    $  203    $  259  
Dividends on preference shares...         2         2         5         5   
                                     ------    ------    ------    ------

NET INCOME ATTRIBUTABLE  
 TO COMMON SHAREHOLDERS..........    $   84    $  114    $  198    $  254
                                     ------    ------    ------    ------
</TABLE>


                                       2
<PAGE>   3
                            ALCAN ALUMINIUM LIMITED






<TABLE>
INTERIM CONSOLIDATED STATEMENT OF INCOME (cont'd)                          
(unaudited)

<CAPTION>
Periods ended June 30
(in millions of US$,
 except per share amounts)        Second quarter        Six months
                                  --------------      --------------
                                  1998      1997      1998      1997
                                  ----      ----      ----      ----     

<S>                              <C>       <C>       <C>       <C>  
NET INCOME PER COMMON 
 SHARE (NOTE 4)................. $0.37     $0.50     $0.87     $1.12  
                                 -----     -----     -----     -----  

DIVIDENDS PER COMMON SHARE...... $0.15     $0.15     $0.30     $0.30  
                                 -----     -----     -----     -----

</TABLE>


<TABLE>

INTERIM CONSOLIDATED STATEMENT OF INCOME 
(unaudited)

<CAPTION>

Six months ended June 30
(in millions of US$)                                  1998      1997
                                                      ----      ----  

<S>                                                <C>       <C>    
RETAINED EARNINGS - BEGINNING OF PERIOD                             
As previously reported............................ $ 3,556   $ 3,217
Accounting change (note 1)........................     306         -
                                                   -------   -------  
AS RESTATED.......................................   3,862     3,217

Net income........................................     203       259
Dividends - Common................................      68        68
          - Preference............................       5         5
                                                   -------   -------
          
RETAINED EARNINGS - END OF PERIOD................. $ 3,992   $ 3,403
                                                   -------   ------- 
</TABLE>





                                       3




<PAGE>   4

                            ALCAN ALUMINIUM LIMITED



INTERIM CONSOLIDATED BALANCE SHEET
(unaudited for 1998)

<TABLE>
<CAPTION>
(in millions of US$)                        June 30      December 31
                                               1998             1997
                                            -------      -----------
<S>                                         <C>              <C>

ASSETS

CURRENT ASSETS              
 Cash and time deposits...................  $   440          $   608
 Receivables..............................    1,415            1,292

 Inventories
   Aluminum...............................      784              800
   Raw materials..........................      315              307
   Other supplies.........................      236              234
                                            -------          -------
                                              1,335            1,341
                                            -------          -------
Total current assets......................    3,190            3,241
                                            -------          -------
Deferred charges and other assets.........      447              424
Investments...............................      155              251
Property, plant and equipment
 Cost.....................................   11,948           11,715
 Accumulated depreciation.................    6,439            6,257
                                            -------          -------
                                              5,509            5,458
                                            -------          -------
TOTAL ASSETS..............................  $ 9,301          $ 9,374
                                            -------          -------
</TABLE>
                                       4






<PAGE>   5

                            ALCAN ALUMINIUM LIMITED



INTERIM CONSOLIDATED BALANCE SHEET (cont'd)
(unaudited for 1998)

<TABLE>
<CAPTION>
(in millions of US$,                              June 30      December 31
 except per common share amounts)                    1998             1997
                                                  -------      -----------
<S>                                               <C>              <C>
LIABILITIES AND SHAREHOLDERS' EQUITY

CURRENT LIABILITIES
 Payables.....................................    $ 1,038          $ 1,052
 Short-term borrowings........................        198              238
 Income.and other taxes.......................         49               98
 Debt maturing within one year................         40               36
                                                  -------          -------
                                                    1,325            1,424
                                                  -------          -------
Debt not maturing within one year.............      1,222            1,241
Deferred credits and other liabilities........        609              623
Deferred income taxes.........................        698              969
Minority interests............................         42               43

SHAREHOLDERS' EQUITY
 Redeemable non-retractable 
   preference shares..........................        160              203
 Common shareholders' equity
   Common shares..............................      1,256            1,251
   Retained earnings..........................      3,992            3,556
   Deferred translation adjustments...........         (3)              64
                                                  -------          -------
                                                    5,245            4,871
                                                  -------          -------
Total shareholders' equity....................      5,405            5,074
                                                  -------          -------
TOTAL LIABILITIES AND SHAREHOLDERS' EQUITY....    $ 9,301          $ 9,374
                                                  -------          -------
COMMON SHAREHOLDERS' EQUITY PER COMMON SHARE..    $ 23.05          $ 21.43
                                                  -------          -------
RATIO OF TOTAL BORROWINGS TO EQUITY...........      21:79            23:77
                                                  -------          -------
</TABLE>

                                       5






<PAGE>   6
                            ALCAN ALUMINIUM LIMITED

INTERIM CONSOLIDATED STATEMENT OF CASH FLOWS
(unaudited)

<TABLE>
<CAPTION>
Six months ended June 30 
(in millions of US$)                                 1998           1997
                                                     -----          -----
<S>                                                  <C>            <C>
OPERATING ACTIVITIES
 Net income......................................    $ 203          $ 259

 Adjustments to determine cash
   from operating activities:
     Depreciation...............................       223            217
     Deferred income taxes......................        33             (6)
     Equity income - net of dividends...........        44              3
     Change in operating working capital........      (183)          (262)
     Change in deferred charges, 
       other assets, deferred credits
       and other liabilities - net..............       (42)            (4)
     Gain on sales of businesses - net .........        (1)           (13)
     Other - net................................         3             22
                                                     -----          -----
CASH FROM OPERATING ACTIVITIES..................       280            216
                                                     -----          -----
FINANCING ACTIVITIES
 New debt.......................................         8             35
 Debt repayments................................       (14)           (34)
                                                     -----          -----
                                                        (6)             1

 Short-term borrowings - net...................        (38)            77
 Common shares issued...........................         5              9
 Redemption of preference shares................       (43)             -
 Dividends - Alcan shareholders
             (including preference).............       (73)           (73)
           - Minority interests.................        (1)            (2)
                                                     -----          -----
CASH FROM (USED FOR) FINANCING ACTIVITIES.......      (156)            12
                                                     -----          -----
</TABLE>


                                       6




<PAGE>   7

                            ALCAN ALUMINIUM LIMITED



<TABLE>
INTERIM CONSOLIDATED STATEMENT OF CASH FLOWS (cont'd)
(unaudited)

<CAPTION>

Six months ended June 30 
(in millions of US$)                                    1998           1997
                                                        ----           ----
<S>                                                     <C>            <C>

INVESTMENT ACTIVITIES
 Property, plant and equipment.......................   (292)          (230)
 Investments.........................................     (2)             -
 Net proceeds from disposal of
   businesses and other assets.......................      2             48
                                                        ----           ----

CASH USED FOR INVESTMENT ACTIVITIES..................   (292)          (182)
                                                        ----           ----

Effect of exchange rate changes
 on cash and time deposits...........................     (1)             -  
                                                        ----           ---- 

INCREASE (DECREASE) IN CASH AND TIME DEPOSITS........   (169)            46
Cash of companies consolidated (deconsolidated)......      1            (11)
Cash and time deposits 
 - beginning of period...............................    608            546  
                                                        ----           ----  

Cash and time deposits
 - end of period.....................................   $440           $581
                                                        ----           ----

</TABLE>


                                       7




<PAGE>   8

                            ALCAN ALUMINIUM LIMITED


INFORMATION BY PRODUCT SECTOR
(unaudited)

Periods ended June 30
(in millions of US$)

SECOND QUARTER
<TABLE>
<CAPTION>

                                 SALES AND OPERATING REVENUES   OPERATING INCOME
                                -----------------------------   ----------------
                                Intersector     Third parties    
                                -----------     -------------
                                1998     1997    1998    1997    1998     1997
                                ----     ----    ----    ----    ----     ----
<S>                             <C>     <C>      <C>    <C>      <C>      <C>
Raw materials and 
chemicals.....................  $ 124   $ 131   $  129  $  126   $  30    $  31
Primary metal.................    358     378      322     383      85      136
Fabricated products...........      -       -    1,533   1,499      88       94
Intersector and 
 other items..................   (482)   (509)       2       3      37      (19)
                                -----   -----   ------  ------   -----    -----
                                $   -   $   -   $1,986  $2,011   $ 240    $ 242
                                -----   -----   ------  ------

Reconciliation to net income
 Equity income (loss)........                                    $ (23)   $  (1)
 Corporate offices...........                                      (34)     (27)
 Interest....................                                      (21)     (26)
 Income taxes................                                      (76)     (72)
                                                                 -----    -----
 NET INCOME..................                                    $  86    $ 116 
                                                                 -----    -----
</TABLE>

SIX MONTHS
<TABLE>
<CAPTION>

                                SALES AND OPERATING REVENUES    OPERATING INCOME
                                ----------------------------    ----------------
                                Intersector      Third parties    
                                -------------    -------------
                                1998     1997    1998     1997     1998    1997
                                ----     ----    ----     ----     ----    ----
<S>                            <C>      <C>      <C>      <C>      <C>    <C>

Raw materials and
 chemicals...................  $  256   $  244   $  266   $  246   $  69  $  39
Primary metal................     731      769      675      756     215    302
Fabricated products..........       -        -    2,993    2,871     164    159
Intersector and 
 other items.................    (987)  (1,013)       5        8      56    (14)
                               ------   ------   ------   ------   -----  -----  
                               $    -   $    -   $3,939   $3,881   $ 504  $ 486
                               ------   ------   ------   ------      

Reconciliation to net income
 Equity income (loss)........                                      $ (39) $   2
 Corporate offices...........                                        (64)   (61)
 Interest....................                                        (44)   (51)
 Income taxes................                                       (154)  (117)
                                                                   -----  ------  
 NET INCOME..................                                      $ 203  $ 259
                                                                   -----  ------  
</TABLE>

                                       8



<PAGE>   9
                            ALCAN ALUMINIUM LIMITED


            NOTES TO INTERIM CONSOLIDATED FINANCIAL STATEMENTS
                               JUNE 30, 1998
                                (UNAUDITED)

              (in millions of US$, except per share amounts)



1.   ACCOUNTING CHANGE

     In 1998, the Company adopted new recommendations of the Canadian Institute
     of  Chartered Accountants dealing with accounting for income taxes.  The
     principal change under the new recommendations is the requirement to
     revalue deferred income tax liabilities for all changes in tax rates and
     exchange rates.

     The Company has adopted the new recommendations retroactively without
     restating prior years.  The cumulative effect of adopting the new
     recommendations at January 1, 1998 is to decrease Deferred income taxes by
     $285 million, to increase Retained earnings by $306 million and to decrease
     Deferred translation adjustments by $21 million.


2.   DIFFERENCES BETWEEN CANADIAN AND UNITED STATES GENERALLY ACCEPTED
     ACCOUNTING PRINCIPLES (GAAP)

     Differences in 1998 relate principally to accounting for foreign currency
     translation.  Differences prior to 1998 relate principally to accounting
     for deferred income taxes.


     RECONCILIATION OF CANADIAN AND U.S. GAAP


<TABLE>
<CAPTION>
                                             1998                 1997    
                                      -----------------     ---------------
                                         AS        U.S.        As      U.S.
                                      REPORTED     GAAP     Reported   GAAP
                                      --------     ----     --------   ----
<S>                                    <C>       <C>        <C>      <C>
     Net income

     First quarter................     $  117    $  117     $  143   $  142
     Second quarter...............         86        94        116      141
                                       ------    ------     ------   ------
     Six months...................     $  203    $  211     $  259   $  283
                                       ------    ------     ------   ------
     Net income attributable
       to common shareholders.....     $  198    $  206     $  254   $  278
                                       ------    ------     ------   ------
     Net income per common share
       Basic and diluted..........     $ 0.87    $ 0.91     $ 1.12   $ 1.23
                                       ------    ------     ------   ------

</TABLE>


                                       9
<PAGE>   10

RECONCILIATION OF CANADIAN AND U.S. GAAP (CONT'D)

<TABLE>
<CAPTION>
                                               1998                      1997
                                       ---------------------------------------------
                                          AS         U.S.          As           U.S.
                                       REPORTED      GAAP       Reported        GAAP
                                       --------      ----       --------        ----
<S>                                    <C>         <C>           <C>          <C>
Comprehensive income *
   First quarter.....................      n/a     $   111           n/a      $    61
   Second quarter....................      n/a     $    54           n/a      $   178
                                       -------     -------       -------      -------
   Six months........................      n/a     $   165           n/a      $   239
                                       -------     -------       -------      -------
Deferred income taxes 
        - June 30....................  $   698     $   698       $   977      $   722
                                       -------     -------       -------      -------
Retained earnings
        - June 30....................  $ 3,992     $ 4,033       $ 3,403      $ 3,730
                                       -------     -------       -------      -------
Deferred translation
   adjustments - June 30.............  $   (3)     $  (43)       $   176      $    98
                                       -------     -------       -------      -------
<FN>
   *   Beginning in 1998, U.S. GAAP requires the disclosure of comprehensive
       income which, for the Company, is Net income under U.S. GAAP plus the
       movement in Deferred translation adjustments under U.S. GAAP.  The
       concept of comprehensive income does not exist under Canadian GAAP.
</FN>
</TABLE>

3. INCOME TAXES
<TABLE>
<CAPTION>
                                          Second quarter              Six months   
                                         ----------------         -----------------
                                         1998        1997          1998        1997
                                         ----        ----          ----        ----
<S>                                      <C>         <C>           <C>         <C>
Current................................  $ 58        $ 76          $ 121       $ 123
Deferred...............................    18          (4)            33          (6)
                                         ----        ----          -----       -----
                                         $ 76        $ 72          $ 154       $ 117
                                         ----        ----          -----       -----
</TABLE> 

     The composite of the applicable statutory corporate income tax rates in
Canada is 40.4% (40.3% for 1997).

     The difference between income taxes calculated at the composite rate and
the amounts shown as reported is attributable mainly to exchange and the large
corporations tax, partially offset by investment and other allowances.  In 1997,
the difference is mainly attributable to prior years' tax adjustments and
investment and other allowances.



                                       10
<PAGE>   11

4.   NET INCOME PER COMMON SHARE

     Net income per common share is based on the average number of shares
     outstanding during the period (second quarter 1998: 227.5 million; 
     1997: 227.0 million; six months 1998: 227.5 million; 1997: 226.9 million).
     As at June 30, 1998, there were 227,538,313 common shares outstanding.  
 
 
5.   SUPPLEMENTARY INFORMATION
   
     STATEMENT OF CASH FLOWS
     <TABLE>   
     <CAPTION>
                                         Second quarter           Six months
                                        -----------------      ----------------- 
                                         1998       1997        1998       1997
                                        ------     ------      ------     ------    
     <S>                                <C>        <C>         <C>        <C>
     Interest paid..................    $   21     $   22      $   49     $   50
     Income taxes paid..............    $   96     $   70      $  185     $  130
                                        ------     ------      ------     ------   
     </TABLE>

     SUMMARIZED FINANCIAL INFORMATION

     The following is summarized consolidated financial information for Alcan
     Aluminum Corporation, a wholly-owned subsidiary in the United States.
  
     <TABLE>
     <CAPTION>
                                         Second quarter           Six months
                                        -----------------      ----------------- 
                                         1998       1997        1998       1997
                                        ------     ------      ------     ------   
     <S>                                <C>        <C>         <C>        <C>
     RESULTS OF OPERATIONS
     Revenues......................     $  996     $  954      $1,908     $1,819
     Costs and expenses............        912        897       1,759      1,737
                                        ------     ------      ------     ------   

     Income before incomes taxes...         84         57         149         82
     Income taxes..................         33         22          59         32
                                        ------     ------      ------     ------   

     Net income....................     $   51     $   35      $   90     $   50
                                        ------     ------      ------     ------   
     </TABLE>


     <TABLE>
     <CAPTION>
                                                        JUNE 30      December 31
                                                          1998           1997
                                                      -----------    -----------  
     <S>                                              <C>            <C>   
     FINANCIAL POSITION
     Current assets...............................      $  852         $  801
     Current liabilities..........................         456            376 
                                                        ------         ------  
    
     Working capital..............................         396            425
     Property, plant and equipment - net..........         716            736
     Other liabilities - net......................         (49)          (199)
                                                        ------         ------  
                                                         1,063            962
     Debt not maturing within one year............         102            102
                                                        ------         ------  
     Net assets...................................      $  961         $  860
                                                        ------         ------  
     </TABLE>


                                       11




<PAGE>   12
     In the above figures, inventories have been valued principally by the
     last-in, first-out (LIFO) method.  In the Company's consolidated financial
     statements, the average cost method is used.

6.   SUBSEQUENT EVENT

     On July 3, 1998, the Company acquired an additional 17% of Indian Aluminium
     Company, Limited (Indal), and will acquire a further 3% on completion of
     certain Indian tax formalities, for a total of $70 million in cash. This
     will bring Alcan's stake in Indal to 54.6%.

7.   PRIOR YEAR AMOUNTS

     Certain prior year amounts have been reclassified to conform with the 1998
     presentation.


     In the opinion of management, all adjustments necessary for a fair
presentation of interim period results have been included in the financial
statements.  These interim results are not necessarily indicative of results for
the full year.



                                       12

<PAGE>   13
<TABLE>

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


RESULTS OF OPERATIONS

<CAPTION>

                                       SECOND           SIX          FIRST
                                       QUARTER         MONTHS       QUARTER
                                     ------------    -----------    -------  
Highlights (US$ millions,            1998    1997    1998    1997     1998
  except per share amounts)          ----    ----    ----    ----     ----          

<S>                                 <C>     <C>     <C>     <C>      <C>
  Sales and operating revenues....  1,986   2,011   3,939   3,881    1,953  

  Net income......................     86     116     203     259      117  
  Net income per common share.....   0.37    0.50    0.87    1.12     0.50  

</TABLE>



     The Company reports second quarter consolidated net income of US$113
million (49 cents per share) before losses at its Japanese affiliate, compared
to $118 million (51 cents per share) in the corresponding quarter of 1997. After
a charge of $27 million (12 cents per share) for losses at 45.6%-owned Nippon
Light Metal Company, Ltd. (NLM) net income for the quarter ended June 30, 1998
was $86 million versus $116 million in the second quarter of 1997. After
preference share dividends, net income per common share for the quarter is 37
cents compared to 50 cents a year earlier.

     Alcan's share of the equity-accounted losses at NLM referred to above
includes restructuring costs of $16 million (7 cents per share). NLM's losses
have no impact on Alcan's cash flows. The maximum amount of losses which Alcan
may be required to record in the future is limited to the net book value of its
investment in NLM. At current exchange rates, the net book value of Alcan's
investment in NLM now stands at $88 million.

     Fabricated product operations in Europe and North America performed well,
despite the lower commodity price environment, with total fabricated product
shipments up 7% from the previous quarter. Alcan's Japanese affiliate, however,
posted increased operating losses and restructuring costs in the light of very
weak economic conditions.

     Although market conditions remain satisfactory in Europe and North America,
the price for aluminum is unlikely to improve until there are signs of economic
recovery in Japan. Good progress is being made in Alcan's Full Business
Potential program, with a further $40 million achieved in the first half of this
year. The Company is on track to achieve the targeted $300 million earnings
improvement by the end of 1999.

     During the quarter, a 5 1/2-year wage agreement was negotiated with a
majority of Alcan's unionized employees in Quebec, under the 18-year 'no
interruption' agreement announced earlier this year.



                                       13
<PAGE>   14

<TABLE>
<CAPTION>
                                                     SECOND           SIX        FIRST
                                                     QUARTER         MONTHS     QUARTER
                                                   ------------   ------------  ------- 
Volumes (thousands of tonnes)                       1998   1997    1998   1997    1998
                                                   -----  -----   -----  -----   ----- 
<S>                                                <C>    <C>     <C>    <C>     <C>
  Shipments
     Ingot products*..............................   207    216     409    428     202
     Fabricated products..........................   469    448     905    859     436
  Fabrication of customer-owned metal.............    72     73     140    140      68
                                                   -----  -----   -----  -----   -----
  Total volume....................................   748    737   1,454  1,427     706
                                                   =====  =====   =====  =====   =====

  Ingot product realizations (US$ per tonne)...... 1,591  1,770   1,630  1,733   1,670
  Fabricated product realizations (US$ per tonne). 2,930  2,990   2,969  2,980   3,010  
<FN>
  *Includes primary and secondary ingot and scrap
</FN>
</TABLE>

     Sales and operating revenues for the second quarter of 1998 showed a slight
increase over the first quarter, despite lower metal prices, reflecting higher
fabricated product volumes.

     Total fabricated product volumes, which include products fabricated from
customer-owned metal, reached a record level of 541 thousand tonnes (kt) in the
second quarter, some 4% higher than a year earlier and 7% ahead of the first
quarter of 1998.

     Average ingot product realizations declined $79/tonne from the first
quarter and $179/tonne from the second quarter of 1997 compared to declines of
$93 and $218 respectively in the LME 3-month price.

     Fabricated product realizations also declined by less than the drop in
ingot prices compared to a year ago reflecting higher local currency prices in
Europe.

PRODUCT SECTOR REVIEW

     The Company reports selected information by major product sector, viewed on
a stand-alone basis. Transactions between product sectors are conducted on an
arm's length basis and reflect market-related prices. Thus, profit on all
alumina produced by the Company, whether sold to third parties or used in the
Company's smelters, is included in the raw materials and chemicals sector.
Similarly, income from primary metal operations is mainly profit on metal
produced by the Company, whether sold to third parties or used in the Company's
fabricating operations. Income from fabricated product businesses represents
only the fabricating profit on rolled products and downstream businesses.

                                      14



<PAGE>   15
<TABLE>
<CAPTION>

                                           SECOND           SIX         FIRST
                                           QUARTER         MONTHS      QUARTER
                                        ------------    ------------   -------   
(US$ millions)                          1998    1997    1998    1997     1998  

<S>                                      <C>    <C>     <C>     <C>      <C>
  Operating income
     Raw materials and chemicals.....     30      31      69      39       39  
     Primary metal...................     85     136     215     302      130  
     Fabricated products.............     88      94     164     159       76  
     Intersector and other items.....     37     (19)     56     (14)      19  
                                        ----    ----    ----    ----     ----
                                         240     242     504     486      264  

  Equity income (loss)...............    (23)     (1)    (39)      2      (16)
  Corporate offices..................    (34)    (27)    (64)    (61)     (30)
  Interest...........................    (21)    (26)    (44)    (51)     (23)
  Income taxes.......................    (76)    (72)   (154)   (117)     (78) 
                                        ----    ----    ----    ----     ----
  Net income.........................     86     116     203     259      117  
                                        ====    ====    ====    ====     ====
</TABLE>

     Operating profits from raw material and chemical operations were little
changed from the year-ago quarter with lower prices offset by cost savings.
Earnings declined from the first quarter as the effect of lower metal prices
flowed through to alumina.

     The decline in earnings from primary metal operations compared to the first
quarter of 1998 and the year-ago quarter results primarily from lower market
prices for ingot.

     The continued improvement in results from fabricated product businesses
reflects further increases in volume in Europe and North America, partially
offset by weaker results from Asia and South America.

     "Intersector and other items" primarily reflects the realization or
deferral of profits on intersector sales of metal. Profits were deferred in 1997
due to generally rising ingot prices. In the first half of 1998 previously
deferred profits on intersector sales were realized as ingot prices decreased.
Also included in this category is interest income.

     Alcan recorded a loss from equity-accounted companies of $23 million for
the second quarter primarily arising at NLM in Japan. Business conditions in
Japan remain difficult and NLM's operating results deteriorated further. The
continuing review of operations resulted in further provisions for manpower
reductions, with Alcan's share of restructuring costs amounting to $16 million
in the quarter, $27 million year-to-date.

     The effective tax rate rose in the second quarter of 1998 due principally
to higher earnings in countries with higher tax rates and foreign exchange rate
fluctuations.

                                      15


<PAGE>   16
<TABLE>

GEOGRAPHIC REVIEW

<CAPTION>
                                                 SECOND           SIX          FIRST
                                                 QUARTER         MONTHS       QUARTER
                                              ------------    ------------    -------     
Net income (Loss) (US$ millions)              1998    1997    1998    1997      1998  
                                              ----    ----    ----    ----      ----
<S>                                           <C>     <C>     <C>     <C>       <C> 
     Canada................................     34      46      81     131        47  
     United States.........................     41      40      72      66        31  
     South America.........................      1       5       6      19         5  
     Europe................................      5      15      29      27        24  
     Asia and Pacific......................    (17)      7     (23)     20        (6)
     Other  (including eliminations).......     22       3      38      (4)       16  
                                              ----    ----    ----    ----      ---- 
     Net income                                 86     116     203     259       117  
                                              ====    ====    ====    ====      ====
</TABLE>

     In Canada, net income declined from the first quarter and the prior year
due to the effect of lower metal prices on primary metal operations.

     In the United States, net income from operations continued to improve
reflecting strong fabricated product volumes, offset in part by lower profits
on primary metal produced in that country.

     Operating results in South America were affected by lower primary metal
prices and seasonally weaker shipments of rolled products in the second
quarter.

     European results were lower reflecting lower prices for alumina and metal.
Fabricated products, however, improved over the year earlier quarter.

     Results in the Asia and Pacific region for the quarter reflect poor
results from Japan as well as lower alumina prices.

     The profit from "Other" in the quarter arises principally from the
recognition of previously deferred profits on inter-regional sales of ingot. In
1997 this result was adverse as profits were deferred in a generally rising
metal price environment.


LIQUIDITY AND CAPITAL RESOURCES

OPERATING ACTIVITIES

     Cash generated from operating activities during the first half of 1998 was
$280 million, compared to $216 million in the comparable period of 1997. This
is primarily due to a smaller increase in operating working capital reflecting
improved working capital turnover.

FINANCING ACTIVITIES

     Cash used for financing activities in the first half of 1998 was $156
million compared to an inflow in the comparable period of 1997 of $12 million.
During the half year, the Company redeemed $43 million Series 'D' preference
shares and repaid $44 million of debt. The debt:equity ratio at June 30, at
21:79 is unchanged 


                                       16
<PAGE>   17
from the level at March 31, 1998 and compares to 23:77 a year ago. Total
borrowings at June 30,1998 were $1,460 million compared to $1,532 million a year
earlier.

     At the end of the second quarter of 1998, the Company had cash and time
deposits of $440 million, reduced from $608 million at the beginning of the
year.


INVESTMENT ACTIVITIES

     Capital expenditures during the first half of 1998 were $294 million,
compared to $230 million a year earlier. The investment of $1.6 billion in a new
375 kt/y aluminum smelter at Alma, Quebec has commenced, with expenditure of
approximately $200 million anticipated in the current year and most of the
remaining expenditure falling into 1999 and 2000. The year- ago period also
included $48 million of proceeds from disposal of businesses and other assets.

     On July 3, 1998 the Company acquired an additional 17% of Indian Aluminium
Company, Limited (Indal), and is in the process of acquiring a further 3% which
requires completion of certain Indian tax formalities. The total cost of this
additional 20% is $70 million in cash and it will bring Alcan's stake in Indal
to 54.6%.


FINANCIAL INSTRUMENTS - CURRENCY HEDGING FOR ALMA SMELTER

     Through a combination of option contracts and forward exchange contracts
totalling $932 million at June 30, 1998, and maturing over various periods in
1998 and 1999, the Company has hedged its future Canadian dollar commitments for
the construction of the new smelter at Alma, Quebec.

     The present hedging position for the Alma project will ensure that the
Company will pay, on average, no more than $0.72 for Can$1.00, and will be able
to benefit, in part, from any future reductions in the value of the Canadian
dollar.

     Any gains or losses from these hedging activities, and related costs, will
be included in the capital cost of the new smelter.


YEAR 2000 COMPLIANCE

     Alcan continues to implement the various elements of its Year 2000 project.
Remediation, which involves the repair or replacement of systems internal to
Alcan that are not Year 2000 compliant, is under way and the Company believes it
is making good progress with its remediation efforts. The Company continues to
assess its vulnerability to third parties. If remediation by Alcan, or those
with which Alcan does business, is not made in a timely way, then business
interruptions or delays might occur that could have a material adverse effect on
Alcan's business and financial condition. Costs associated with Year 2000
systems remediation at Alcan facilities, based on information currently
available, are estimated to be US$50 million. Such costs are being expensed as
incurred over the 1998 and 1999 periods.

                                      17
<PAGE>   18
PART II. -- OTHER INFORMATION

ITEMS 1. THROUGH 5.

     The registrant has nothing to report under these items.

ITEM 6.   EXHIBITS AND REPORTS ON FORM 8-K

          (a)  Exhibits

               (27) Financial Data Schedule. (Filed herewith.)

               (99) Cautionary statement for purposes of the "Safe Harbor"
                    provisions of the Private Securities Litigation Reform Act
                    of 1995. (Filed herewith.)

          (b)  Reports on Form 8-K 

               None were filed in the quarter ended June 30, 1998.


                                   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.


                                   ALCAN ALUMINIUM LIMITED



Dated: August 13, 1998             By:  /s/ Geoffrey P. Batt
                                       --------------------------
                                       Geoffrey P. Batt
                                       Treasurer
                                       (A Duly Authorized Officer)


                                      18

<PAGE>   19
                                 EXHIBIT INDEX


Exhibit 
Number                            Description

(27)      Financial Data Schedule.

(99)      Cautionary statement for purposes of the "Safe Harbor"
          provisions of the Private Securities Litigation Reform Act of 1995.