<PAGE>
 
                                   FORM 10-Q
                      SECURITIES AND EXCHANGE COMMISSION
                             Washington, DC  20549


                  QUARTERLY REPORT UNDER SECTION 13 OR 15(d)
                    OF THE SECURITIES EXCHANGE ACT OF 1934


For Quarter Ended  March 31, 1998                Commission File Number 1-10040
                  ----------------                                     ---------


                         CYPRUS AMAX MINERALS COMPANY
--------------------------------------------------------------------------------
            (Exact name of registrant as specified in its charter)



          Delaware                                             36-2684040
--------------------------------------------------------------------------------
(State or other jurisdiction of                             (I.R.S. Employer
 incorporation or organization)                          Identification Number)



9100 East Mineral Circle, Englewood, Colorado                    80112
--------------------------------------------------------------------------------
(Address of principal executive offices)                       (Zip Code)


                                (303) 643-5000
--------------------------------------------------------------------------------
             (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 
                                        ---     ---    

Number of shares of common stock outstanding as of May 13, 1998, was 93,655,814
shares.


                         This report contains 22 pages.

                                      -1-
<PAGE>
 
                        PART I.   FINANCIAL INFORMATION
                        -------------------------------

ITEM 1.   FINANCIAL STATEMENTS
------------------------------

                 CYPRUS AMAX MINERALS COMPANY AND SUBSIDIARIES
                     CONSOLIDATED STATEMENT OF OPERATIONS
                      (IN MILLIONS EXCEPT PER SHARE DATA)


                                                       (Unaudited)
                                                      Three Months
                                                     Ended March 31,
                                                    -----------------
                                                      1998     1997
                                                    --------  ------- 

REVENUE                                             $    732  $   888
                                                    --------  -------
COSTS AND EXPENSES
Cost of Sales                                            534      542 
Selling and Administrative Expenses                       27       30 
Depreciation, Depletion, and Amortization                107       98 
Write-Downs and Special Charges                            -      116 
Exploration Expense                                       10        6 
                                                    --------  ------- 
TOTAL COSTS AND EXPENSES                                 678      792 
                                                    --------  ------- 
INCOME FROM OPERATIONS                                    54       96 

OTHER INCOME (EXPENSE)                                                
Interest Income                                            4        9 
Interest Expense                                         (48)     (51)
Capitalized Interest                                       1        6 
Equity Investments and Other                               -       (3)
                                                    --------  ------- 
INCOME BEFORE INCOME TAXES AND MINORITY INTEREST          11       57 

Income Tax Provision                                      (6)       - 
Minority Interest                                          -        - 
                                                    --------  ------- 
NET INCOME                                                 5       57 
Preferred Stock Dividends                                 (5)      (5)
                                                    --------  ------- 
INCOME APPLICABLE TO COMMON SHARES                  $      -  $    52 
                                                    ========  =======  
                                                                      
EARNINGS PER COMMON SHARE                                             
  Basic                                             $      -  $   .56 
                                                    ========  =======  
  Diluted                                           $      -  $   .56 
                                                    ========  =======  
 
AVERAGE COMMON SHARES OUTSTANDING
  Basic                                                 93.7     93.4
  Diluted                                              103.3    103.1


See accompanying notes to consolidated financial statements.

                                      -2-
<PAGE>
 
                 CYPRUS AMAX MINERALS COMPANY AND SUBSIDIARIES
                          CONSOLIDATED BALANCE SHEET
                      (IN MILLIONS EXCEPT SHARE AMOUNTS)

<TABLE>
                                                             (Unaudited)
                                                              March 31,   December 31,
                                                                 1998         1997
                                                              ----------  -------------
<S>                                                           <C>         <C>
                        ASSETS
CURRENT ASSETS
Cash and Cash Equivalents                                        $  292         $  250
Accounts and Notes Receivable, Net                                  218            201
Inventories                                                         540            526
Prepaid Expenses                                                    113            147
Deferred Income Taxes                                                11              8
                                                                 ------         ------
  Total Current Assets                                            1,174          1,132
PROPERTIES - At Cost, Net                                         4,926          4,978
OTHER ASSETS                                                        334            349
                                                                 ------         ------
  Total Assets                                                   $6,434         $6,459
                                                                 ======         ======
            LIABILITIES AND SHAREHOLDERS' EQUITY
CURRENT LIABILITIES
Short-Term Debt                                                  $   72         $   55
Current Portion of Long-Term Debt                                   208            180
Accounts Payable                                                    131            139
Accrued Payroll and Benefits                                         94            100
Accrued Royalties and Interest                                       75             50
Accrued Closure, Reclamation and Environmental                       58             59
Other Accrued Liabilities                                           127            143
Taxes Payable, Other Than Income Taxes                               77             67
Income Taxes Payable                                                 19             23
Dividends Payable                                                    19             19
                                                                 ------         ------
  Total Current Liabilities                                         880            835
                                                                 ------         ------
NONCURRENT LIABILITIES AND DEFERRED CREDITS
Long-Term Debt                                                    2,075          2,089
Capital Lease Obligations                                            82            113
Deferred Employee and Retiree Benefits                              405            407
Deferred Closure, Reclamation and Environmental                     348            352
Deferred Income Taxes                                                62             57
Other                                                               112            117
                                                                 ------         ------
  Total Noncurrent Liabilities and Deferred Credits               3,084          3,135
                                                                 ------         ------
MINORITY INTEREST                                                   157            159
SHAREHOLDERS' EQUITY
Preferred Stock, $1 Par Value,
  20,000,000 Shares Authorized:
  $4.00 Series A Convertible Stock, $50 Stated Value,
    4,666,667 Authorized, 4,664,302 Issued and Outstanding
    in 1998 and 1997                                                  5              5
  Series A Preferred Stock, 500,000 Shares
    Authorized, None Issued or Outstanding                            -              -
Common Stock, Without Par Value,
  150,000,000 Shares Authorized,
  Issued 96,031,034 in 1998 and 96,031,038 in 1997                    1              1
Paid-In Surplus                                                   2,943          2,947
Accumulated Deficit                                                (523)          (504)
Other                                                                (8)            (8)
                                                                 ------         ------
                                                                  2,418          2,441
Treasury Stock at Cost, 2,356,151 Shares in 1998
  and 2,548,867 Shares in 1997                                      (54)           (58)
Loan to Savings Plan                                                (51)           (53)
                                                                 ------         ------
  Total Shareholders' Equity                                      2,313          2,330
                                                                 ------         ------
  Total Liabilities and Shareholders' Equity                     $6,434         $6,459
                                                                 ======         ======
</TABLE>

See accompanying notes to consolidated financial statements.

                                      -3-
<PAGE>
 
                 CYPRUS AMAX MINERALS COMPANY AND SUBSIDIARIES
                     CONSOLIDATED STATEMENT OF CASH FLOWS
                                 (IN MILLIONS)

 
                                                         (Unaudited)
                                                        Three Months
                                                       Ended March 31,
                                                      -----------------
                                                        1998     1997
                                                      --------  -------

CASH FLOWS FROM OPERATING ACTIVITIES
Net Income                                              $   5    $  57
  Depreciation, Depletion, and Amortization               107       98
  Write-Downs and Special Charges                           -      116
  Deferred Income Taxes                                     2      (10)
  Gain on Sale of Assets                                    -     (137)
  Changes in Assets and Liabilities Net of Effects
    from Businesses Acquired/Sold                          25       48
  Other, Net                                                8        9
                                                        -----    -----
NET CASH PROVIDED BY OPERATING ACTIVITIES                 147      181
                                                        -----    -----
CASH FLOWS FROM INVESTING ACTIVITIES
  Capital Expenditures                                    (67)    (130)
  Capitalized Interest                                     (1)      (6)
  Advances to and Investments in Affiliates               (15)      (3)
  Proceeds from Sale of Assets                              2      107
                                                        -----    -----
NET CASH USED FOR INVESTING ACTIVITIES                    (81)     (32)
                                                        -----    -----
CASH FLOWS FROM FINANCING ACTIVITIES
  Net Proceeds from Issuance of Long-Term Debt              3       16
  Net Borrowings on Short-Term Debt                        17        -
  Payments on Short-Term Debt                               -      (15)
  Payments on Long-Term Debt and Other Obligations        (18)      (5)
  Dividends Paid                                          (23)     (23)
  Dividends to Minority Interests                          (3)      (2)
                                                        -----    -----
NET CASH USED FOR FINANCING ACTIVITIES                    (24)     (29)
                                                        -----    -----
NET INCREASE IN CASH AND CASH EQUIVALENTS                  42      120
CASH AND CASH EQUIVALENTS AT BEGINNING OF YEAR            250      193
                                                        -----    -----
CASH AND CASH EQUIVALENTS AT END OF PERIOD              $ 292    $ 313
                                                        =====    =====
 
Non-Cash Investing Activity:
  Note received for Coal Contract                       $   -    $  31
                                                        =====    =====
 

See accompanying notes to consolidated financial statements.

                                      -4-
<PAGE>
 
                 CYPRUS AMAX MINERALS COMPANY AND SUBSIDIARIES
                  NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


NOTE 1.  BASIS OF PRESENTATION
------------------------------

The accompanying interim unaudited financial statements include all adjustments
which are, in the opinion of management, necessary for a fair presentation.
Results for any interim period are not necessarily indicative of the results
that may be achieved in future periods.  The financial information as of this
interim date should be read in conjunction with the financial statements and
notes thereto contained in Cyprus Amax's Annual Report on Form 10-K for the year
ended December 31, 1997.

NOTE 2.  INVENTORIES
--------------------

Inventories detailed by component are summarized below (in millions):

                                    (Unaudited)
                                     March 31,   December 31,
                                       1998          1997
                                    -----------  ------------
Component
  In-Process Ores, Concentrates,
    and Other                            $ 246          $ 234
  Finished Goods                           172            178
  Materials and Supplies                   122            114
                                         -----          -----
                                         $ 540          $ 526
                                         =====          =====

NOTE 3.  FAIR VALUE OF FINANCIAL INSTRUMENTS
--------------------------------------------

The estimated fair values of financial instruments under SFAS No. 107,
"Disclosures About Fair Value of Financial Instruments," are made at discrete
points in time based on relevant market information.  These estimates involve
uncertainties and cannot be determined with precision.  At March 31,1998, the
net carrying value of financial instruments approximated a $1,721 million
liability, whereas the fair value approximated a $1,692 million liability.  The
difference in fair value is primarily due to the volatility in the copper market
and a decrease in copper prices which have increased the value of the copper
price protection programs, offset by lower interest rates as of March 31, 1998
compared to rates on the Company's debt.

NOTE 4.  CONTINGENCIES
----------------------

Cyprus Tohono Mining Company was informed in late 1995 by the office of the
Assistant U.S. Attorney in Tucson, Arizona that an action was being considered
under federal environmental laws against Cyprus Tohono Corporation and certain
of its employees.  The facts giving rise to this matter involved a break in the
process line at Tohono occurring in 1992.  It is not possible to state with
reasonable certainty at this time what action will be taken by the government.

Cyprus Miami and other companies, in conjunction with the Arizona Department of
Environmental Quality's Water Quality Assurance Revolving Fund program,
continued remediation and assessment of ground water quality at Pinal Creek near
Miami, Arizona throughout 1997.  Despite the fact that the ongoing program,
initiated in 1989, has resulted in continued improvement of sub-surface water
quality in the area, Cyprus Miami was informed that the State of Arizona was
contemplating enforcement action against Cyprus Miami and/or other companies in
connection with the Pinal Creek water quality issues under federal and state
environmental laws. On November 10, 1997, Cyprus Miami, as a member of the Pinal
Creek group, joined with the State of Arizona in seeking approval of the
District Court for entry of a Consent Decree to resolve all matters related to
the contemplated enforcement action. The Decree commits Cyprus Amax and other
Pinal

                                      -5-
<PAGE>
 
Creek group members to complete the work outlined in the remedial action plan
submitted to the State in May 1997.  The Final Remediation Action Plan will be
finalized through provisions of the Decree.  Approximately $40 million remained
in the Pinal Creek remediation reserve at March 31, 1998.  Cyprus Miami has
commenced contribution litigation against other parties involved in this matter
and has asserted claims against certain of its past insurance carriers.  While
significant recoveries are expected, Cyprus Miami cannot reasonably estimate the
amount and, therefore, has not taken potential recoveries into consideration in
the recorded reserve.

At March 31, 1998, Cyprus Amax had accruals of approximately $406 million for
expected future mine closure, reclamation, and environmental remediation
liabilities.  Total reclamation costs for Cyprus Amax at the end of current mine
lives are estimated at about $625 million.  Additionally, the cost range of
reasonably possible outcomes for sites where remediation costs are estimable is
from $65 million to $280 million of which approximately $100 million was
reserved at March 31, 1998.  Work on these sites is expected to be substantially
completed in the next several years, subject to the inherent delays involved in
the process. Remediation costs that could not be reasonably estimated at March
31, 1998, are not expected to have a material impact on the financial condition
and ongoing operations of the Company.

NOTE 5.  INFORMATION BY INDUSTRY SEGMENT
----------------------------------------

Cyprus Amax operates in three principal industry segments -- Copper/Molybdenum,
Coal, and Other -- which supply mineral products primarily to the construction,
automobile, steel, and utility industries and gold to banks and other bullion
dealers.  The financial information for these segments is presented below (in
millions):
 
                                            (Unaudited)   
                                           Three Months   
                                          Ended March 31, 
                                          --------------  
                                           1998     1997  
                                          -----    -----  
     Segment Revenue                                      
                                                          
      Copper/Molybdenum                   $ 335    $ 394  
      Coal                                  303      431  
      Other                                  94       63  
                                          -----    -----  
                                                          
                                          $ 732    $ 888  
                                          =====    =====  
                                                          
     Segment Operating Income (Loss)                      
                                                          
      Copper/Molybdenum                   $  38    $  87  
      Coal                                   30       25  
      Other                                  (2)      (3) 
                                          -----    -----  
                                                          
                                             66      109  
                                                          
     Corporate                              (12)     (13) 
     Interest, Net                          (43)     (36) 
     Equity Investments and Other             -       (3) 
                                          -----    -----  
                                                          
      Income Before Income Taxes                          
       and Minority Interest                 11       57  
     Income Tax Provision                    (6)       -  
     Minority Interest                        -        -  
                                          -----    -----  
                                                          
      Net Income                          $   5    $  57  
                                          =====    =====   

                                      -6-
<PAGE>
 
REVIEW BY INDEPENDENT ACCOUNTANTS
---------------------------------

The financial information as of March 31, 1998, and for the three-month periods
ended March 31, 1998 and 1997, included in Part I pursuant to Rule 10-01 of
Regulation S-X has been reviewed by Price Waterhouse LLP, the Company's
independent accountants, in accordance with standards established by the
American Institute of Certified Public Accountants.  Price Waterhouse LLP's
report is included as page 8 of this quarterly report.

Price Waterhouse LLP does not carry out any significant or additional audit
tests beyond those which would have been necessary if its report had not been
included in this quarterly report. Accordingly, such report is not a "report" or
"part of a registration statement" within the meaning of Sections 7 and 11 of
the Securities Act of 1933 and the liability provisions of Section 11 of such
Act do not apply.

                                      -7-
<PAGE>
 
                       REPORT OF INDEPENDENT ACCOUNTANTS
                       ---------------------------------


To the Board of Directors and Shareholders of Cyprus Amax Minerals Company

We have reviewed the accompanying consolidated balance sheet of Cyprus Amax
Minerals Company and its subsidiaries as of March 31, 1998, and the related
consolidated statements of operations and of cash flows for the three-month
periods ended March 31, 1998 and 1997. These financial statements are the
responsibility of the Company's management.

We conducted our review in accordance with standards established by the American
Institute of Certified Public Accountants.  A review of interim financial
information consists principally of applying analytical procedures to financial
data and making inquiries of persons responsible for financial and accounting
matters.  It is substantially less in scope than an audit conducted in
accordance with generally accepted auditing standards, the objective of which is
the expression of an opinion regarding the financial statements taken as a
whole.  Accordingly, we do not express such an opinion.

Based on our review, we are not aware of any material modifications that should
be made to the accompanying interim financial information for it to be in
conformity with generally accepted accounting principles.

We previously audited in accordance with generally accepted auditing standards,
the consolidated balance sheet as of December 31, 1997, and the related
consolidated statements of operations, of shareholder's equity, and of cash
flows for the year then ended (not presented herein), and in our report dated
February 11, 1998, we expressed an unqualified opinion on those consolidated
financial statements.  In our opinion, the information set forth in the
accompanying consolidated balance sheet information as of December 31, 1997, is
fairly stated in all material respects in relation to the consolidated balance
sheet from which it has been derived.



Price Waterhouse LLP

Denver, Colorado
May 14, 1998

                                      -8-
<PAGE>
 
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS OF OPERATIONS AND
-------------------------------------------------------------------------
FINANCIAL CONDITION
-------------------

To the extent the company makes forward-looking statements, actual results may
vary materially therefrom. All of the information set forth in this Form 10-Q,
including without limitation the Cautionary Statement and Risk Factors described
herein, should be considered and evaluated.

RESULTS OF OPERATIONS
---------------------

CYPRUS AMAX MINERALS COMPANY  reported consolidated net income of $5 million, or
break-even earnings per share, on revenue of $732 million for the first quarter
of 1998, compared with 1997 earnings of $57 million, or 56 cents per share, on
revenue of $888 million.  The 1997 amounts included an after-tax gain of $29
million or 28 cents per share for a favorable tax adjustment resulting from
settlement of certain prior year tax issues and the impact of coal settlements,
reduced to recognize certain provisions for mine closing costs.

Excluding the above-mentioned gain, lower 1998 first quarter earnings resulted
from lower copper and gold realizations, partially offset by substantially
improved coal performance and lower copper and gold production costs.

                                                             March 31,
                                                        ------------------
SELECTED RESULTS (In millions except per share data)      1998      1997
                                                        --------  --------
Revenue                                                  $ 732     $ 888
Net Income                                               $   5     $  57
Earnings Per Share                                       $   -     $ .56

The 1998 first quarter revenue of $732 million was $156 million lower than the
comparable 1997 quarter primarily due to $137 million of gains recorded on the
settlements of certain coal contracts in 1997 and lower metals realizations,
partially offset by higher gold sales.

POTENTIAL DISPOSITIONS

On February 9, 1998, Amax Gold announced that it entered into a merger agreement
with Kinross Gold Corporation whereby each share of Amax Gold Common Stock will
be converted into 0.8 of a share of Kinross Common Stock.  Cyprus Amax will
exchange $135 million of cash and indebtedness of Amax Gold at the effective
time of the merger for approximately 35 million shares of Kinross Common Stock.
The merger is expected to close on June 1, 1998, and Cyprus Amax will own
approximately 31 percent of the new Kinross. This merger will result in the
deconsolidation of Amax Gold and Kinross will be accounted for as an equity
investment.

On February 24, 1998, Cyprus Amax signed a letter of intent to sell selected
Appalachian and Midwestern coal properties to AEI Holding Company, Inc (AEI).
The sale is expected to be completed during the second quarter of 1998.

On April 27, 1998, Cyprus Amax reached a definitive agreement to sell its Cyprus
Foote Mineral Company lithium subsidiary to an affiliate of Chemetall GmbH, a
specialty chemicals unit of Metallgesellschaft AG.  The sale is contingent upon
regulatory approvals, with closing to take place as soon as possible.

Proceeds from the above-mentioned sales will be used to strengthen Cyprus Amax's
financial position and core mining businesses.

                                      -9-
<PAGE>
 
SEGMENT RESULTS

Segment income is earnings before corporate overhead, interest, equity and
other, income taxes, and minority interest.

COPPER/MOLYBDENUM
                                                        Three Months Ended
                                                             March 31,
                                                        ------------------
SELECTED RESULTS (In millions)                            1998      1997
                                                        --------  --------
Revenue                                                  $ 335     $ 394

Segment Operating Income                                 $  38     $  87

COPPER/MOLYBDENUM earned $38 million during the first quarter, $49 million lower
than in the 1997 period. Lower earnings reflected 23 cents or 21 percent lower
copper realizations and $10 million lower molybdenum results, partially offset
by seven cents per pound lower costs of copper sold.

First quarter copper realizations averaged 87 cents per pound, 23 cents lower
than in the 1997 quarter.  Cyprus Amax has price protection programs in place
that will ensure a minimum net average realization on an LME basis at March 31,
1998, of 88 cents per pound on 265 million pounds for the balance of 1998.
Cyprus Amax had previously sold 19 million pounds of first quarter 1998 copper
price protection contracts. This sale, along with the copper price protection
program, favorably improved first quarter 1998 operating earnings by $21
million. As of May 13, 1998 Cyprus Amax has approximately 216 million pounds of
copper price protection at 88 cents per pound for the remainder of 1998.

                                                        Three Months Ended
                                                             March 31,
                                                        ------------------
OTHER OPERATING DATA (In millions except as noted)        1998      1997
                                                        --------  --------

Copper Sales Volume, Pounds                                273       266 
Produced Copper Sold, Pounds                               243       251  
Copper Production, Pounds                                  234       241   
 
Average Copper Realization, $/Pound                      $ .87     $1.10   
Cost of Sales, $/Pound                                   $ .75     $ .82   
Net Cash Cost, $/Pound                                   $ .57     $ .64   
Full Cost, $/Pound                                       $ .72     $ .76   
                                                                           
Bagdad                                                                     
------
Production - Pounds                                         52        58   
Material Mined - Tons                                     15.8      18.7   
Ore Mined - Tons                                           6.9       7.0   
Ore Milled - Tons                                          7.3       7.2   
Ore Grade - %                                              .36       .43   
                                                                           
Miami                                                                      
-----
Production - Pounds                                         41        34   
Material Mined - Tons                                     23.5      24.6   
Ore Mined - Tons                                           8.7       8.1   
Ore Grade - %                                              .29       .52    
 
 

                                      -10-
<PAGE>
 
                                                        Three Months Ended
                                                             March 31,
                                                        ------------------
OTHER OPERATING DATA (In millions except as noted)        1998      1997
                                                        --------  --------
Sierrita
--------
Production - Pounds                                         55        60   
Material Mined - Tons                                     23.6      23.1    
Ore Mined - Tons                                           9.5      10.4    
Ore Milled - Tons                                          9.7      10.5    
Ore Grade - %                                              .27       .27     

Cerro Verde
-----------
Production - Pounds                                         31        30
Material Mined - Tons                                      7.9       9.2
Ore Mined - Tons                                           2.4       2.0
Ore Grade - %                                              .82       .86 
 
El Abra
-------
Production - Pounds (51%)                                   53        49   
Material Mined - Tons (100%)                               9.4       8.2    
Ore Mined - Tons (100%)                                    8.9       8.3    
Ore Grade - %                                              .78       .95    
                                                                            
Molybdenum Sales - Pounds                                   16        16    
Produced Molybdenum Sold - Pounds                           16        16    
Molybdenum Production - Pounds                              15        16    
Average Realization - $/Pound                            $5.08     $5.58    
                                                                            
Henderson                                                                   
---------
Production - Pounds                                          8        10    
Material Mined - Tons                                      1.8       2.0    
Ore Milled - Tons                                          1.8       2.0    
Ore Grade - %                                              .25       .26     


During the quarter, Cyprus Amax sold 243 million pounds of produced copper, 8
million pounds lower than in the 1997 first quarter.  Cost of sales decreased
seven cents per pound from the 1997 period to 75 cents per pound for the first
quarter of 1998 reflecting lower worldwide costs.

First quarter net cash costs for copper decreased to 57 cents per pound from 64
cents per pound for the first quarter of 1997, a reduction of 11 percent,
primarily reflecting lower cash costs at all operations in spite of lower
domestic production.

Copper production totaled 234 million pounds for the quarter compared to 241
million pounds in 1997.  The slight decrease in production was in accordance
with our plan to reduce higher cost domestic sulfide ore production until copper
prices improve.

In January 1998, Cyprus Amax reached an agreement with the Highlands Pacific
Group to acquire up to 75 percent of its 86 percent interest in the Frieda River
copper and gold exploration project in Papua New Guinea. Cyprus Amax is
committed under the agreement to spend up to $7 million on resource drilling and
further engineering studies in 1998 and, if Cyprus Amax elects to proceed to the
next stage of exploration and development, up to a total of $32 million to
complete the feasibility study.

                                      -11-
<PAGE>
 
Primary molybdenum operations earned $10 million for the first quarter of 1998
compared with $20 million for the year earlier period.  Production of 15 million
pounds was 1 million pounds lower than the comparable 1997 quarter, and produced
sales of 16 million pounds were comparable to 1997.  First quarter 1998
realizations, including downstream products, averaged $5.08 per pound compared
to $5.58 per pound during the first quarter of 1997.
 
COAL
                                                        Three Months Ended
                                                             March 31,
                                                        ------------------
SELECTED RESULTS (In millions)                            1998      1997
                                                        --------  --------
Revenue                                                  $ 303     $ 431

Segment Operating Income                                 $  30     $  25


COAL reported first quarter earnings of $30 million compared to 1997 first
quarter earnings of $25 million.  The first quarter of 1997 included a pre-tax
gain of $17 million from the sale and assignment of two coal contracts net of
provisions for mine closure costs and asset write-downs.  Excluding this gain in
1997, earnings from operations improved $22 million.  The increase in earnings
primarily related to the following: Pennsylvania's earnings doubled due to
higher production and shipments plus lower cash costs; and Colorado's earnings
were higher due to lower cash costs resulting from a mine plan that better
controls mining conditions and cost-reduction programs.

In the first quarter of 1998, productivity improved by more than 10 percent over
1997 due to only two longwall moves occurring compared with five in 1997, and
improved planning and control techniques.  As a result of these productivity
improvements, total unit costs of $13.17 per ton were nearly a dollar per ton
lower than in 1997.  The largest improvements were in Pennsylvania, Colorado and
Illinois.  Average realizations improved 20 cents a ton due to a greater
concentration of higher priced contract shipments mainly in Wyoming and Utah.

Additionally, rail service by Union Pacific improved somewhat from the fourth
quarter of 1997. However, slow cycle times reduced shipments by approximately 1
million tons and earnings by $1 million.

                                                        Three Months Ended
                                                             March 31,
                                                        ------------------
SELECTED OPERATING DATA                                   1998      1997
                                                        --------  -------- 
Sales Volume - Millions of Tons
-------------------------------
 Eastern Mines                                               7.2       6.7
 Western Mines - Powder River Basin                          9.8      10.0
 Western Mines - Other                                       3.1       3.1
 Springvale                                                  0.3       0.4
                                                        --------  -------- 
  Total Sales                                               20.4      20.2
                                                        --------  -------- 
 Oakbridge Equity Share                                      1.5       1.3 
Average Realization - $/Ton                               $14.28    $14.08 
Domestic Average Contract Price - $/Ton                   $13.87    $13.44 
Domestic Average Spot Price - $/Ton                       $16.56    $16.60 
Australian Contract Price - $/Ton                         $20.86    $26.58 
Australian Spot Price - $/Ton                             $17.67    $23.39 
Average Cost of Sales - $/Ton                             $13.04    $13.97 
Average Cash Cost - $/Ton                                 $11.41    $12.41 
Average Unit Cost - $/Ton                                 $13.17    $14.14  

                                      -12-
<PAGE>
 
                                                        Three Months Ended
                                                             March 31,
                                                        ------------------
SELECTED OPERATING DATA                                   1998      1997
                                                        --------  --------   
Clean Production - Millions of Tons
-----------------------------------
 Pennsylvania                                                3.3       2.4
 Kentucky                                                    2.0       1.7
 West Virginia                                               1.5       1.9
 Midwest                                                     0.9       1.4
 Wyoming - Powder River                                      9.7      10.1
 Colorado                                                    3.0       2.1
 Utah                                                        0.3       0.5
 Springvale                                                  0.3       0.1
                                                        --------  --------   
                                                                           
  Total Production                                          21.0      20.2
                                                        --------  --------   
                                                                          
 Oakbridge Equity Share                                      1.5       1.0 
 
Coal production of 23 million tons was two million tons higher than in 1997, and
coal sales of 22 million tons in the first quarter of 1998 were comparable to
1997.

Cyprus Amax's equity share in Oakbridge, which is reported in Interest, Equity,
and Other reflected break-even earnings compared to a loss of $3 million in the
1997 comparable quarter.  Improved earnings was due to the absence of the losses
from a high cost mine that was closed and fewer longwall moves.

Ban-Pu, a 6.7 percent shareholder in Oakbridge exercised an option that required
Cyprus Amax to purchase Ban-Pu's shareholding in Oakbridge.  The share purchase,
which increased Cyprus Amax's ownership interest in Oakbridge to 48 percent, was
completed in January 1998 for an investment of approximately $10 million.

Longwall start-up at the Willow Creek mine in Utah is anticipated in the second
quarter of 1998. Approximately $164 million of the mine construction and
development capital was committed through March 31, 1998.
 
OTHER MINERALS

                                                        Three Months Ended
                                                             March 31,
                                                        ------------------
SELECTED DATA (In millions)                               1998      1997
                                                        --------  --------    
 Segment Operating Income (Loss)                        $     (2) $     (3)
                                                        ========  ========
 
 Lithium                                                $      4  $      5
 Amax Gold                                                     8         1
 Businesses Sold/Non-Operating                                (4)       (2)
 Exploration                                                 (10)       (7)
                                                        --------  --------
 Total                                                  $     (2) $     (3)
                                                        ========  ========
 
 Lithium
  Sales Volumes - Millions of Lbs. Carbonate Equiv.           11        11
 Gold (100 percent basis)
  Sales Volumes - Thousands of Ounces                        185        99
  Realized Gold Price - $/Ounce                              338       388

                                      -13-
<PAGE>
 
OTHER MINERALS, which includes Lithium, Amax Gold, Exploration, and Businesses
Sold/Non-Operating, had a combined loss for the first quarter of 1998 of $2
million compared to a loss of $3 million in 1997.  Lithium earned $4 million, $1
million less than in 1997, due primarily to lower carbonate prices.  Exploration
expense of $10 million was $3 million higher than in 1997, principally due to
accelerated drilling on Cyprus Amax's Kansanshi pre-development copper project
in Africa.

Amax Gold's earnings were $8 million compared to $1 million in 1997. The
improvement results from Amax Gold monetizing a portion of its foreign tax net
operating losses resulting in a gain of $7 million. Gold production almost
doubled to 198,000 ounces from 103,000 ounces due to the new production at the
Fort Knox and Kubaka mines and cash costs dropped $46 per ounce to $190 per
ounce reflecting the benefits of this new lower cost production. However, gold
realizations dropped $50 per ounce to $338 per ounce from the 1997 first quarter
to the 1998 comparable quarter. Due to hedging benefits the gold realization of
$338 per ounce was $44 per ounce higher than the average spot price for the
first quarter of 1998.

CORPORATE

Corporate expense of $12 million for the first quarter was $1 million lower than
the 1997 comparable quarter.

INTEREST, EQUITY INVESTMENTS, AND OTHER expense of $43 million for the 1998
first quarter was $4 million higher than the 1997 quarter.  Net interest expense
of $43 million for the first quarter of 1998 was $7 million higher than the same
period in 1997.  Interest expense decreased $3 million to $48 million as a
result of the corporate strategy to reduce debt in 1997.  Capitalized interest
decreased $5 million to $1 million in the first quarter of 1998 due to the
completion of development projects in 1997.  Interest income decreased $5
million in the quarter to $4 million due to lower average cash balances and the 
subordinated note repayment from El Abra to Cyprus Amax.

LIQUIDITY AND CAPITAL RESOURCES

At March 31, 1998, the Company had a ratio of long-term debt to total
capitalization of 48.3 percent, a ratio of current assets to current liabilities
of 1.3 to 1.0, and a cash balance of $292 million.  At December 31, 1997, the
comparable ratios were 49.0 percent and 1.4 to 1.0, respectively.  The Company's
cash balance increased from $250 million at year-end to $292 million at March 31
due primarily to cash provided by continuing operations of $147 million,
partially reduced by capital expenditures of $67 million and dividend payments
of $23 million.

Capital expenditures, excluding capitalized interest, were $67 million for the
first quarter.  Copper expenditures of $27 million included $8 million for the
Henderson 2000 project and the remainder primarily for sustaining and
replacement capital.  Coal expenditures of $33 million included $18 million for
the development of the Willow Creek mine in Utah and the remainder was primarily
for sustaining and replacement capital.  Other Minerals capital expenditures
included expenditures of $4 million for the Refugio and Fort Knox mines.  Total
capital spending for 1998 is projected to be less than $275 million with over 58
percent, 33 percent, and 4 percent spent on copper, coal and gold, respectively.

Taking into consideration the three previously mentioned dispositions, Cyprus
Amax now expects to spend approximately $105 million for reclamation,
remediation, and environmental compliance for the full year 1998.

During 1998, Cyprus Amax expects to be able to generate sufficient funds for
general corporate purposes, capital expenditures, and acquisitions through
internally generated funds, sales of selected assets, and existing or new
borrowings.

Cyprus Amax paid regular dividends of 20 cents per share on its common stock and
$1.00 per preferred share during the quarter.  At March 31, 1998, 93,674,883
shares of the Company's common stock were outstanding.

                                      -14-
<PAGE>
 
CAUTIONARY "SAFE HARBOR" STATEMENT UNDER THE UNITED STATES PRIVATE SECURITIES
LITIGATION REFORM ACT OF 1995

                             CAUTIONARY STATEMENT

With the exception of historical matters, the matters discussed in this report
are forward-looking statements that involve risks and uncertainties that could
cause actual results to differ materially from projected results. Such forward-
looking statements include statements regarding projections of mineral
production levels, such operating costs, capital expenditure levels, certain
significant cost and expenses, price protection programs, percentage increases
and decreases in production from the Company's operations, schedules for
completion of feasibility studies and initial feasibility studies, potential
increases in reserves and production, the timing and scope of future drilling
and other exploration activities, expectations regarding receipt of permits and
commencement of mining or production, anticipated recovery rates, and potential
acquisitions or increases in property interests.  Factors that could cause
actual results to differ materially include changes in relevant mineral prices,
mineral supply contract renegotiations, the presence or absence of price
protection programs, unanticipated ore grade, geological, hydrological,
metallurgical, processing, access, transportation activities, results of pending
and future feasibility studies, operating and development project risks, changes
in project parameters as plans continue to be refined, political, economic, and
operational risks of foreign and domestic operations, joint venture
relationships, competitive conditions, availability of materials and equipment,
the timing and receipt of governmental permits, changes in laws or regulations
or their interpretation and application, force majeure events, the failure of
plant, equipment or processes to operate in accordance with specifications or
expectations, accidents, adverse weather, labor relations, delays in start-up
dates, environmental costs and risks, the outcome of acquisition or disposition
negotiations, and general domestic and international economic and political
conditions, as well as other factors described herein or in the Company's
filings with the U.S. Securities and Exchange Commission.  Many of these factors
are beyond the Company's ability to predict or control.  Readers are cautioned
not to put undue reliance on forward-looking statements.

                                      -15-
<PAGE>
 
PART II--OTHER INFORMATION
--------------------------


ITEM 1.  LEGAL PROCEEDINGS
--------------------------

See Note 4 to Consolidated Financial Statements.

ITEM 2.  CHANGES IN SECURITIES
------------------------------

Not applicable.

ITEM 3.  DEFAULTS UPON SENIOR SECURITIES
----------------------------------------

Not applicable.

ITEM 4.  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS
------------------------------------------------------------

(a)  The annual meeting of shareholders was held on May 6, 1998.

(b)  This information is omitted pursuant to instruction 3.

(c)  Set forth below are the votes cast for the election of Directors:
 
                                 For         Withheld
                              ----------    ---------
 
     William C. Bousquette    81,717,041    2,652,569
     Thomas F. Falkie         81,746,859    2,622,751
     Ann Maynard Gray         81,665,488    2,704,122
     Theodore M. Solso        81,759,310    2,610,400
     James A. Todd, Jr.       81,724,862    2,644,748


     The shareholders also voted to approve the Stock Plan for Non-Employee
     Directors, as amended and restated. Votes cast in favor were 66,187,611,
     against were 17,365,686, abstaining were 816,313. The shareholders voted to
     approve the appointment of Price Waterhouse LLP as Independent Accountants.
     Votes cast in favor were 83,059,956, against were 983,051, and abstaining
     were 326,603.

     The shareholders voted down the shareholder proposal relating to an
     Independent Nominating Committee. Votes cast in favor were 20,472,955,
     against were 49,358,130, abstaining were 2,900,004, and non votes were
     11,638,521.

(d)  Not applicable.

ITEM 5.  OTHER INFORMATION
--------------------------

Amax Oil & Gas, Inc., Union Pacific Oil & Gas Company and Union Pacific
Resources Company ("UPRC") (collectively, the "Defendants") are defendants in
two consolidated actions entitled Stephen H. Parker v. Amax Oil & Gas, Inc. (No.
93-0305578-CV) and Bergstein Oil & Gas Partnership, et al. v. Union Pacific Oil
& Gas Company, et al. (No. 94-10-05721), both filed in the 112th District Court,
Crockett County, Texas (collectively, the 

                                      -16-
<PAGE>
 
"Lawsuits"). Pursuant to the Stock Purchase Agreement dated March 1, 1994
between Amax Coal Company ("Amax Coal") and UPRC, as amended and supplemented by
the Settlement Agreement between Amax Coal and UPRC (collectively, the
"Agreements"), Amax Coal agreed to indemnify and hold UPRC harmless from certain
losses in connection with the Lawsuits. Effective April 23, 1998, the parties to
the Lawsuits and the Company entered into a settlement agreement, whereby the
Company will pay to the Plaintiffs an aggregate settlement amount of $27,000,000
(the "Settlement Payment") in accordance with the Company's indemnification
obligation. The Company expects the Settlement Payment to be made during the
second quarter of 1998. In consideration of the Settlement Payment, UPRC agreed
to provide the Company and its affiliates a general release from the
indemnification obligations that relate to the Lawsuits.

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

(a)  The following Exhibits are filed as part of this Quarterly Report on Form
     10-Q:

         Exhibit
         Number                            Document
        ---------      --------------------------------------------------
          (11)         Statement re computation of per share earnings.
          (15)         Letter re unaudited financial information.
          (27)         Financial data schedule.

(b)  No Current Report on Form 8-K was filed during the quarter ended March 31,
     1998.

                                      -17-
<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.


                                        CYPRUS AMAX MINERALS COMPANY
                                        ----------------------------
                                                 Registrant



Date:  May 14, 1998                           /s/ John Taraba
       ------------                     -----------------------------
                                                 John Taraba
                                        Vice President and Controller
                                        (Principal Accounting Officer)

                                      -18-