<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, 1999    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, 1999, was 90,454,610
                                                                     ----------
shares.

                         This report contains 25 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)
                                        
<TABLE>
<CAPTION>
                                                                                            (Unaudited)
                                                                                            Three Months
                                                                                          Ended March 31,
                                                                                 ----------------------------------
                                                                                       1999              1998
                                                                                 ----------------  ----------------
 
<S>                                                                              <C>               <C>
Revenue                                                                                   $  449            $  732
                                                                                          ------            ------
 
Costs and Expenses
Cost of Sales                                                                                345               534
Selling and Administrative Expenses                                                           18                27
Depreciation, Depletion, and Amortization                                                     73               107
Exploration Expense                                                                            3                10
                                                                                          ------            ------
 
Total Costs and Expenses                                                                     439               678
                                                                                          ------            ------
 
Income from Operations                                                                        10                54
 
Other Income (Expense)
Interest Income                                                                                4                 4
Interest Expense                                                                             (36)              (48)
Capitalized Interest                                                                           1                 1
Equity Investments and Other                                                                 (10)                -
                                                                                          ------            ------
 
Income (Loss) Before Income Taxes and Minority Interest                                      (31)               11
 
Income Tax Benefit (Provision)                                                                 4                (6)
Minority Interest                                                                              1                 -
                                                                                          ------            ------
 
Net Income (Loss)                                                                            (26)                5
 
Preferred Stock Dividends                                                                     (5)               (5)
                                                                                          ------            ------
 
Income (Loss) Applicable to Common Shares                                                 $  (31)           $  -
                                                                                          ======            ======
 
Earnings (Loss) Per Common Share
  Basic                                                                                   $ (.33)           $  -
                                                                                          ======            ======
  Diluted                                                                                 $ (.33)           $  -
                                                                                          ======            ======
 
Average Common Shares Outstanding
  Basic                                                                                     90.4              93.7
  Diluted                                                                                  100.1             103.3
</TABLE>

See accompanying notes to consolidated financial statements.

                                      -2-
<PAGE>
 
                 CYPRUS AMAX MINERALS COMPANY AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEET
                       (In Millions Except Share Amounts)

<TABLE>
<CAPTION>
                                                                                              (Unaudited)
                                                                                               March 31,   December 31,
                                           Assets                                                1999          1998
                                                                                              -----------  -------------
<S>                                                                                           <C>          <C>
Current Assets
Cash and Cash Equivalents                                                                         $  273         $  353
Accounts Receivable, Net                                                                              64             48
Notes Receivable, Net                                                                                 60             69
Inventories                                                                                          381            386
Prepaid Expenses                                                                                      43             52
Deferred Income Taxes                                                                                 16             13
                                                                                                  ------         ------
  Total Current Assets                                                                               837            921
Properties - At Cost, Net                                                                          3,799          3,842
Equity Investments                                                                                   337            345
Other Assets                                                                                         218            233
                                                                                                  ------         ------
  Total Assets                                                                                    $5,191         $5,341
                                                                                                  ======         ======
                               Liabilities and Shareholders' Equity
Current Liabilities
Short-Term Debt                                                                                   $   54         $   35
Current Portion of Long-Term Debt                                                                     97            126
Accounts Payable                                                                                      52             81
Accrued Payroll and Benefits                                                                          72             75
Accrued Royalties and Interest                                                                        57             38
Accrued Closure, Reclamation and Environmental                                                        89             97
Other Accrued Liabilities                                                                             76            126
Taxes Payable, Other Than Income Taxes                                                                62             49
Income Taxes Payable                                                                                  20             25
Dividends Payable                                                                                      5             19
                                                                                                  ------         ------
  Total Current Liabilities                                                                          584            671
                                                                                                  ------         ------
 
Noncurrent Liabilities and Deferred Credits
Long-Term Debt                                                                                     1,678          1,677
Capital Lease Obligations                                                                             41             41
Deferred Employee and Retiree Benefits                                                               349            345
Deferred Closure, Reclamation, and Environmental                                                     280            300
Deferred Income Taxes                                                                                 54             57
Other                                                                                                 55             59
                                                                                                  ------         ------
  Total Noncurrent Liabilities and Deferred Credits                                                2,457          2,479
                                                                                                  ------         ------
 
Minority Interest                                                                                     32             34
 
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 1999 and 1998                                                                                   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 96,031,015 in 1999 and 96,031,015 in 1998                                                     1              1
Paid-In Surplus                                                                                    2,913          2,917
Accumulated Deficit                                                                                 (706)          (672)
Other                                                                                                 (8)            (3)
                                                                                                  ------         ------
                                                                                                   2,205          2,248
Treasury Stock at Cost, 5,577,436 Shares in 1999
  and 5,816,090 Shares in 1998                                                                       (87)           (91)
                                                                                                  ------         ------
  Total Shareholders' Equity                                                                       2,118          2,157
                                                                                                  ------         ------
  Total Liabilities and Shareholders' Equity                                                      $5,191         $5,341
                                                                                                  ======         ======
</TABLE>

See accompanying notes to consolidated financial statements.

                                      -3-
<PAGE>
 
                 CYPRUS AMAX MINERALS COMPANY AND SUBSIDIARIES
                      CONSOLIDATED STATEMENT OF CASH FLOWS
                                 (In Millions)
                                        
<TABLE>
<CAPTION>
                                                                                            (Unaudited)
                                                                                           Three Months
                                                                                          Ended March 31,
                                                                                -----------------------------------
                                                                                      1999              1998
                                                                                ----------------  -----------------
<S>                                                                             <C>               <C>
Cash Flows from Operating Activities
Net Income (Loss)                                                                         $ (26)             $   5
 
  Depreciation, Depletion, and Amortization                                                  73                107
  Deferred Income Taxes                                                                      (7)                 2
  Changes in Assets and Liabilities Net of Effects
    from Businesses Acquired/Sold                                                           (22)                25
  Other, Net                                                                                  8                  8
                                                                                          -----              -----
 
Net Cash Provided by Operating Activities                                                    26                147
                                                                                          -----              -----
 
Cash Flows from Investing Activities
  Capital Expenditures                                                                      (73)               (67)
  Capitalized Interest                                                                       (1)                (1)
  Advances to and Investments in Affiliates                                                  (3)               (15)
  Collections on Notes Receivable                                                             1                  1
  Proceeds from Sale of Assets                                                                3                  1
                                                                                          -----              -----
 
Net Cash Used for Investing Activities                                                      (73)               (81)
                                                                                          -----              -----
 
Cash Flows from Financing Activities
  Net Proceeds from Issuance of Long-Term Debt                                                3                  3
  Net Borrowings on Short-Term Debt                                                          19                 17
  Payments on Long-Term Debt and Other Obligations                                           (3)               (17)
  Payments on Capital Lease Obligations                                                     (30)                (1)
  Dividends Paid                                                                            (22)               (23)
  Dividends to Minority Interests                                                             -                 (3)
                                                                                          -----              -----
 
Net Cash Used for Financing Activities                                                      (33)               (24)
                                                                                          -----              -----
 
Net Increase (Decrease) in Cash and Cash Equivalents                                        (80)                42
Cash and Cash Equivalents at Beginning of Year                                              353                250
                                                                                          -----              -----
 
Cash and Cash Equivalents at End of Period                                                $ 273              $ 292
                                                                                          =====              =====
</TABLE>


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, 1998.

Note 2.  Inventories
--------------------

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

 
<TABLE>
<CAPTION>
                                                                               (Unaudited)
                                                                                March 31,          December 31,
                                                                                  1999                 1998
                                                                           -------------------  ------------------
<S>                                                                        <C>                  <C>
Component
  In-Process Ores, Concentrates,
    and Other                                                                           $ 182                $ 197
  Finished Goods                                                                          131                  120
  Materials and Supplies                                                                   68                   69
                                                                                        -----                -----
                                                                                        $ 381                $ 386
                                                                                        =====                =====
</TABLE>

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 31,1999, the
net carrying value of financial instruments approximated a $1,314 million
liability, whereas the fair value approximated a $1,307 million liability.

Note 4.  Contingencies
----------------------

Cyprus Tohono Corporation 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 involve a break in a
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.

The Pinal Creek Group, comprised of Cyprus Miami Mining Corporation and other
companies, continued remediation and assessment of ground water quality in the
shallow alluvial aquifers along Pinal Creek near Miami, Arizona. The removal,
remediation, and assessment work is being conducted in accordance with the
requirements of the Arizona Department of Environmental Quality's Water Quality
Assurance Revolving Fund program. In addition, the remedial and removal action
is consistent with the National Contingency Plan prepared by the EPA as required
by CERCLA. The ongoing removal, remediation, and assessment program, initiated
in 1989, has resulted in continued improvement of the sub-surface water quality
in the area. In November 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 the entry of a Consent Decree resolving all matters related to an
enforcement action contemplated by the State of Arizona with respect to the
ground water matter. On August 13, 1998, the court approved the Decree that
committed Cyprus Miami and the other Pinal Creek Group members to complete the
remediation work outlined in the remedial action plan that was submitted to the
State in May 1997. Approximately $104 million remained in the Pinal Creek
remediation reserve at March 31, 1999. Cyprus Miami has commenced contribution
litigation against other parties


                                      -5-
<PAGE>
 
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, 1999, Cyprus Amax had accruals of approximately $369 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 $443 million of which approximately $218 million
was reserved at March 31, 1999.  Additionally, the cost range of reasonably
possible outcomes for sites where remediation costs are estimable is from $130
million to $460 million of which approximately $151 million was reserved at
March 31, 1999.  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,
1999, are not expected to have a material impact on the financial condition and
ongoing operations of the Company.

                                      -6-
<PAGE>
 
Note 5.  Information by Operating Segment
-----------------------------------------

Cyprus Amax adopted SFAS No. 131, "Disclosures about Segments of an Enterprise
and Related Information" for the year ended December 31, 1998.  The segment
information for 1998 has been restated from the prior year's presentation in
order to conform to the 1999 presentation.  The Company's reportable segments
are strategic business units that offer different products and services.  They
are managed separately because each business requires different technology and
marketing strategies.  Cyprus Amax's three reportable segments in 1999 are
Copper/Molybdenum, Coal, and Exploration.  The Copper/Molybdenum segment mines,
processes, and markets copper and molybdenum primarily in North, Central, and
South America.  The Coal segment mines, cleans, markets, and sells coal to
electric utilities and industrial users.  The Exploration segment seeks a range
of mineral opportunities from early stage generative exploration through
advanced opportunities and acquisitions and conducts exploration programs around
its developing and producing mines to find and delineate ore that could extend
the lives of those operations.

Cyprus Amax evaluates performance based on profit or loss from operations before
interest income and expense, income taxes, and minority interest.  There are no
intersegment sales between reportable segments.

Summarized financial information concerning the Company's reportable segments is
shown in the following tables. In 1998, All Other includes the segments Lithium,
Amax Gold, and Businesses Sold/Non-Operating that were below the quantitative
thresholds to be reportable segments. In 1999 All Other only includes Businesses
Sold/Non-Operating as the Lithium and Amax Gold businesses were sold or merged
in 1998.

<TABLE>
<CAPTION>
                                                                                            (Unaudited)
                                                                                           Three Months
(In Millions)                                                                             Ended March 31,
                                                                                -----------------------------------
                                                                                      1999               1998
                                                                                -----------------  ----------------
<S>                                                                             <C>                <C>
Segment Revenue
 
  Copper/Molybdenum                                                                        $ 276             $ 335
  Coal                                                                                       172               303
  All Other                                                                                    1                94
                                                                                           -----             -----
 
                                                                                           $ 449             $ 732
                                                                                           =====             =====
 
Segment Operating Income (Loss)
 
  Copper/Molybdenum                                                                        $   7             $  38
  Coal                                                                                        19                30
  Exploration                                                                                 (3)              (10)
  All Other                                                                                   (2)                8
                                                                                           -----             -----
 
                                                                                              21                66
 
Corporate                                                                                    (11)              (12)
Interest, Net                                                                                (31)              (43)
Equity Investments and Other                                                                 (10)                -
                                                                                           -----             -----
 
  Income (Loss) Before Income Taxes
    and Minority Interest                                                                    (31)               11
Income Tax Benefit (Provision)                                                                 4                (6)
Minority Interest                                                                              1                 -
                                                                                           -----             -----
 
  Net Income (Loss)                                                                        $ (26)            $   5
                                                                                           =====             =====
</TABLE>

                                      -7-
<PAGE>
 
Review by Independent Accountants
---------------------------------

The financial information as of March 31, 1999, and for the three-month periods
ended March 31, 1999 and 1998, included in Part I pursuant to Rule 10-01 of
Regulation S-X has been reviewed by PricewaterhouseCoopers LLP, the Company's
independent accountants, in accordance with standards established by the
American Institute of Certified Public Accountants.  PricewaterhouseCoopers
LLP's report is included as page 9 of this quarterly report.

PricewaterhouseCoopers 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.

                                      -8-
<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, 1999, and the related
consolidated statements of operations and of cash flows for the three-month
periods ended March 31, 1999 and 1998. 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, 1998, and the related
consolidated statements of operations, of shareholders' equity, and of cash
flows for the year then ended (not presented herein), and in our report dated
February 11, 1999, 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, 1998, is
fairly stated in all material respects in relation to the consolidated balance
sheet from which it has been derived.



/s/ PricewaterhouseCoopers LLP

Denver, Colorado
May 14, 1999

                                      -9-
<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 a consolidated net loss of $26 million, or
33 cents per share, on revenue of $449 million for the first quarter of 1999,
compared with 1998 earnings of $5 million, or break-even earnings per share, on
revenue of $732 million.

The decrease in 1999 first quarter earnings resulted from lower metal
realizations, reduced coal and equity investment earnings, and the absence of
earnings from the coal properties and the Lithium and Amax Gold businesses that
were sold or merged in 1998, partially offset by substantially lower copper
production costs and lower exploration and interest costs.

<TABLE>
<CAPTION>
                                                                                       Three Months Ended
                                                                                            March 31,
                                                                                ---------------------------------
Selected Results (In millions except per share data)                                  1999             1998
                                                                                ----------------  ---------------
 
<S>                                                                             <C>               <C>
Revenue                                                                                   $ 449             $ 732
 
Net Income (Loss)                                                                         $ (26)            $   5
 
Earnings (Loss) Per Share                                                                 $(.33)            $  -

</TABLE>
The 1999 first quarter revenue of $449 was $283 million lower than the
comparable 1998 quarter primarily due to the impact of the coal properties sold
in 1998, lower metals and coal realizations, the deconsolidation of Amax Gold in
the second quarter of 1998 as a result of its merger with Kinross Gold, lower
coal and molybdenum sales volumes and the sale of the Lithium business in the
fourth quarter of 1998, partially offset by higher produced copper sales
volumes.

Potential Dispositions

On October 22, 1998, Cyprus Amax's Board of Directors approved the engagement of
Salomon Smith Barney to undertake a possible sale of Cyprus Amax Coal Company.
On May 13, 1999, Cyprus Amax announced it had reached a definitive agreement to
sell its Cyprus Amax Coal subsidiary to RAG International Mining GmbH. The
boards of Cyprus Amax and RAG have approved the sale, which is subject to
regulatory approvals and other customary conditions, with closing to take place
as soon as possible. Cyprus Amax expects to receive total consideration of
approximately $1.1 billion, consisting of cash and assumption of debt. The buyer
is assuming other long-term obligations and is acquiring related assets. In
addition, Cyprus Amax may receive certain production payments from the Willow
Creek mine. Proceeds from this transaction are expected to be used to reduce
debt, fund the existing share buyback program, continue to strengthen Cyprus
Amax's financial position, and support growth opportunities in its core mining
business.

Segment Results

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

                                      -10-
<PAGE>
 
Copper/Molybdenum
<TABLE>
<CAPTION>
                                                                                       Three Months Ended
                                                                                           March 31,
                                                                                --------------------------------
Selected Results (In millions)                                                       1999             1998
                                                                                ---------------  ---------------
 
<S>                                                                             <C>              <C>
Revenue                                                                                   $ 276            $ 335
 
Segment Operating Income                                                                  $   7            $  38
</TABLE>

Copper/Molybdenum earned $7 million during the first quarter, $31 million lower
than in the 1998 period. Lower earnings reflected 21 cents or 24 percent lower
copper realizations and $7 million lower molybdenum results, partially offset by
11 cents per pound lower costs of copper sold and higher produced copper sales.

First quarter copper realizations averaged 66 cents per pound, 21 cents lower
than in the 1998 quarter.  The first quarter 1998 earnings was benefited by $21
million from the copper price protection program.  At March 31, 1999, Cyprus
Amax had no price protection programs in place.  

<TABLE>
<CAPTION>
                                                                                       Three Months Ended
                                                                                           March 31,
                                                                                --------------------------------
Other Operating Data (In millions except as noted)                                   1999             1998
                                                                                ---------------  ---------------
 
<S>                                                                             <C>              <C>
Copper Sales Volume, Pounds                                                                 304              273
Produced Copper Sold, Pounds                                                                286              243
Copper Production, Pounds                                                                   254              234
 
Average Copper Realization, $/Pound                                                       $ .66            $ .87
Cost of Sales, $/Pound                                                                    $ .64            $ .75
Net Cash Cost, $/Pound                                                                    $ .49            $ .57
Full Cost, $/Pound                                                                        $ .62            $ .72
 
Bagdad
------
Production - Pounds                                                                          60               52
Material Mined - Tons                                                                      15.8             15.8
Ore Mined - Tons                                                                            7.6              6.9
Ore Milled - Tons                                                                           7.4              7.3
Ore Grade - %                                                                               .39              .36
 
Miami
-----
Production - Pounds                                                                          39               41
Material Mined - Tons                                                                      16.2             23.5
Ore Mined - Tons                                                                            3.3              8.7
Ore Grade - %                                                                               .50              .29
 
Sierrita
--------
Production - Pounds                                                                          60               55
Material Mined - Tons                                                                      19.0             23.6
Ore Mined - Tons                                                                            9.5              9.5
Ore Milled - Tons                                                                           9.7              9.7
Ore Grade - %                                                                               .29              .27
</TABLE> 

                                      -11-
<PAGE>
 
<TABLE> 
<CAPTION> 
                                                                                       Three Months Ended
                                                                                           March 31,
                                                                                --------------------------------
Other Operating Data (In millions except as noted - continued)                       1999             1998
                                                                                ---------------  ---------------
 
<S>                                                                             <C>              <C>
Cerro Verde
-----------
Production - Pounds                                                                          36               31
Material Mined - Tons                                                                       9.8              7.9
Ore Mined - Tons                                                                            3.4              2.4
Ore Grade - %                                                                               .80              .82
 
El Abra
-------
Production - Pounds (51%)                                                                    59               53
Material Mined - Tons (100%)                                                               13.0              9.4
Ore Mined - Tons (100%)                                                                    10.0              8.9
Ore Grade - %                                                                               .81              .78
 
Molybdenum Sales - Pounds                                                                    14               16
Produced Molybdenum Sold - Pounds                                                            14               16
Molybdenum Production - Pounds                                                               16               15
Average Realization - $/Pound                                                             $4.14            $5.08
 
Henderson
---------
Production - Pounds                                                                           8                8
Material Mined - Tons                                                                       1.7              1.8
Ore Milled - Tons                                                                           1.7              1.8
Ore Grade - %                                                                               .26              .25
</TABLE>

During the quarter, Cyprus Amax sold 286 million pounds of produced copper, 43
million pounds more than in the 1998 first quarter.  Cost of sales decreased 11
cents per pound from the 1998 period to 64 cents per pound for the first quarter
of 1999 reflecting lower costs at all operations.

First quarter net cash costs for copper decreased to 49 cents per pound from 57
cents per pound for the first quarter of 1998, a reduction of 14 percent,
primarily reflecting lower cash costs at all operations and record low smelting
and refining costs. Excluding the by-product credit, net cash costs were 11
cents per pound lower.

Copper production totaled 254 million pounds for the quarter compared with 234
million pounds in 1998.  The higher production was from both the domestic and
South American mines due to productivity improvements.

For the quarter, the Miami smelter and refining complex set a record for
throughput, cost, and quality.  Costs were the lowest on record with the smelter
operating at 115 percent of design capacity and the refinery about 110 percent
of its designed output.

In accordance with the agreement for the Kansanshi copper project in Zambia, a
decision by Cyprus Amax to continue on into the second phase was due by March
14, 1999.  However, due to the low copper price environment an extension on the
decision was granted until June 9, 1999.

In accordance with the 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 declared a force majeure
due to low copper prices.  Therefore, the completion of Phase I has been delayed
until the force majeure is removed.

Primary molybdenum operations earned $3 million for the first quarter of 1999
compared with $10 million for the year earlier period.  Production of 16 million
pounds was 1 million pounds higher than the comparable 1998 quarter and produced
sales of 14 million pounds were 2 million pounds lower than the first quarter of

                                      -12-
<PAGE>
 
1998.  First quarter 1999 realizations, including downstream products, averaged
$4.14 per pound compared with $5.08 per pound during the first quarter of 1998.

The Henderson 2000 project at the primary molybdenum mine in Colorado remains on
budget and on schedule. The Henderson mine is expected to shut down for about
three months beginning in the third quarter of 1999 in order to complete the
change over to a conveyor system from a rail haulage system.

Coal
<TABLE>
<CAPTION>
                                                                                       Three Months Ended
                                                                                            March 31,
                                                                                ---------------------------------
Selected Results (In millions)                                                       1999              1998
                                                                                ---------------  ----------------
 
<S>                                                                             <C>              <C>
Revenue                                                                                   $ 172             $ 303
 
Segment Operating Income                                                                  $  19             $  30
</TABLE>

Coal reported first quarter earnings of $19 million compared to 1998 first
quarter earnings of $30 million. The decrease in earnings was primarily related
to the absence of operating earnings from the properties sold to AEI in the
second quarter of 1998 and the continued recovery efforts resulting from the
underground fire at the Willow Creek mine that occurred in late 1998 that cost
$6 million in the quarter.


<TABLE>
<CAPTION>
                                                                                       Three Months Ended
Selected Operating Data                                                                    March 31,
                                                                                --------------------------------
                                                                                     1999             1998
                                                                                ---------------  ---------------
<S>                                                                             <C>              <C>
Sales Volume - Millions of Tons
-------------------------------
 
  Eastern Mines                                                                             3.0              7.2
  Western Mines - Powder River Basin                                                        9.1              9.8
  Western Mines - Other                                                                     2.6              3.1
  Springvale                                                                                0.2              0.3
                                                                                         ------           ------
     Total Sales                                                                           14.9             20.4
                                                                                         ------           ------
 
  Oakbridge Equity Share                                                                    1.4              1.5
 
Average Realization - $/Ton                                                              $11.25           $14.28
 
Domestic Average Contract Price - $/Ton                                                  $10.62           $13.87
Domestic Average Spot Price - $/Ton                                                      $13.23           $16.56
Australian Contract Price - $/Ton                                                        $18.68           $20.86
Australian Spot Price - $/Ton                                                            $14.83           $17.67
 
Average Cost of Sales - $/Ton                                                            $10.24           $13.04
Average Cash Cost - $/Ton                                                                $ 8.81           $11.41
Average Unit Cost - $/Ton                                                                $ 9.98           $13.17
</TABLE> 

                                      -13-
<PAGE>
 
<TABLE> 
<CAPTION> 
                                                                                          Three Months Ended
                                                                                               March 31,
                                                                                       -------------------------
                                                                                           1999           1998
                                                                                       -----------     ---------
<S>                                                                                    <C>             <C> 
Clean Production - Millions of Tons
-----------------------------------
  Pennsylvania                                                                              3.2              3.3
  Kentucky                                                                                    -              2.0
  West Virginia                                                                               -              1.5
  Midwest                                                                                   0.3              0.9
  Wyoming - Powder River                                                                    9.1              9.7
  Colorado                                                                                  2.7              3.0
  Utah                                                                                      0.3              0.3
  Springvale                                                                                0.1              0.3
                                                                                         ------           ------
 
     Total Production                                                                      15.7             21.0
                                                                                         ------           ------
 
  Oakbridge Equity Share                                                                    1.1              1.5
</TABLE>

The 1998 first quarter statistics for average realizations, cost of sales, cash
costs, and unit costs decreased 17 to 21 percent per ton due to the properties
sold.  Following are the above statistics restated for all periods presented to
exclude the sold properties.

<TABLE>
<CAPTION>
                                                                                       Three Months Ended
Selected Operating Data                                                                    March 31,
                                                                                --------------------------------
 
                                                                                     1999             1998
                                                                                ---------------  ---------------
<S>                                                                             <C>              <C>
Average Realization - $/Ton                                                              $11.25           $11.87
Average Cost of Sales - $/Ton                                                            $10.24           $10.67
Average Cash Costs - $/Ton                                                               $ 8.81           $ 9.02
Average Unit Costs - $/Ton                                                               $ 9.98           $10.83
</TABLE>

Coal production of 17 million tons and coal sales of 16 million tons were 6
million tons lower than in 1998 primarily due to the coal properties sold to AEI
in 1998.  Excluding the properties sold, production was one million tons lower
than 1998, and sales were two million tons lower.  The Powder River Basin's
lower production and sales were a result of a decision to participate less
heavily in the spot market and to utilize only the most efficient stripping
equipment.

The first quarter of 1999 reflected one longwall move at Springvale whereas the
1998 first quarter had two longwall moves, one each at Cumberland and
Springvale. It is anticipated that three longwall moves will occur in the 1999
second quarter.

During the quarter, the Willow Creek mine continued recovery efforts from the
underground fire. Limited continuous miner production resumed at Willow Creek in
late March 1999 and the longwall is expected to be operational late in the third
quarter. The losses that have and are being incurred are expected to be
partially offset by insurance recoveries. Such insurance proceeds are reflected
in income as claims are settled.

Cyprus Amax's equity share in Oakbridge's earnings, which is reported in Equity
Investments and Other reflected a loss of $5 million compared with break-even
earnings in the 1998 comparable quarter.  The loss is due primarily to the
effects of an Australian dollar hedge book that should be mostly closed out by
the end of 1999.

                                      -14-
<PAGE>
 
Exploration

Selected Results (In Millions)
<TABLE>
<CAPTION>
                                                                                            Three Months Ended
                                                                                                 March 31,
                                                                                          -----------------------
                                                                                           1999              1998
                                                                                          -----             -----
<S>                                                                                       <C>               <C>
Segment Operating Loss                                                                    $  (3)            $ (10)
</TABLE>

Exploration expense of $3 million was $7 million lower than in 1998, principally
due to constraining exploration spending in 1999 in response to low copper
prices, primarily for Cyprus Amax's Kansanshi pre-development copper project in
Africa and the Frieda River copper and gold project, and the absence of Amax
Gold expenditures.

All Other
<TABLE>
<CAPTION>
                                                                                        Three Months Ended
                                                                                            March 31,
                                                                                ----------------------------------
Selected Data (In millions)                                                           1999              1998
                                                                                ----------------  ----------------
 
<S>                                                                             <C>               <C>
Segment Operating Income (Loss)                                                           $  (2)            $   8
                                                                                          =====             =====
 
  Lithium                                                                                 $   -             $   4
  Amax Gold                                                                                   -                 8
  Businesses Sold/Non-Operating                                                              (2)               (4)
                                                                                          -----             -----
  Total                                                                                   $  (2)            $   8
                                                                                          =====             =====
 
  Lithium
    Sales Volumes - Millions of Lbs. Carbonate Equiv.                                         -                11
  Gold (100 percent basis)
    Sales Volumes - Thousands of Ounces                                                       -               185
    Gold Price - $/Ounce                                                                      -               338
</TABLE>

All Other, which includes Lithium, Amax Gold, and Businesses Sold/Non-Operating
in 1998 and only Businesses Sold/Non-Operating in 1999, had a combined loss for
the first quarter of 1999 of $2 million compared to earnings of $8 million in
1998.  The decrease in earnings was primarily due to the sale of the Lithium
business in the fourth quarter of 1998 and the deconsolidation of Amax Gold in
the second quarter of 1998.

Corporate expense of $11 million for the first quarter was $1 million lower than
the 1998 comparable quarter.

Interest, Equity Investments, and Other expense of $41 million for the 1999
first quarter was $2 million lower than the 1998 quarter.  Net interest expense
of $31 million for the first quarter of 1999 was $12 million lower than the same
period in 1998.  Interest expense decreased $12 million to $36 million
reflecting the significant reduction in debt.  Equity Investments and Other
reflected a loss of $10 million compared with break-even earnings in 1998.
Oakbridge reported a loss of $5 million compared with break-even earnings in
1998.  The loss is due to the effects of an Australian dollar hedge book, which
should be mostly closed out by the end of 1999.  Additionally, equity losses of
$3 million and $2 million for Kinross and Amax Metals Recovery Inc.,
respectively, were included.  Kinross' loss is attributable to the current low
gold prices.

Liquidity and Capital Resources

At March 31, 1999, the Company had a ratio of long-term debt to total
capitalization of 44.8 percent, a ratio of current assets to current liabilities
of 1.4 to 1.0, and a cash balance of $273 million.  At December 31, 1998, the
comparable ratios were 44.3 percent and 1.4 to 1.0, respectively.  The Company's
cash balance decreased from $353 million at year-end to $273 million at March 31
due primarily to capital expenditures 

                                      -15-
<PAGE>
 
of $73 million, net debt payments of $11 million, and dividend payments of $22
million, partially offset by cash provided by operations of $26 million.

Capital expenditures, excluding capitalized interest, were $73 million for the
first quarter.  Copper expenditures of $46 million included $33 million for the
Henderson 2000 project and the remainder primarily for sustaining and
replacement capital.  Coal expenditures of $27 million included $20 million for
the development of the infrastructure required to access the Northeast reserves
at the Emerald mine in Pennsylvania and the remainder was primarily for
sustaining and replacement capital.  Total capital spending for 1999 is
projected to be about $250 million with over 80 percent and 18 percent spent on
copper and coal, respectively.  If the sale of the Coal Company does occur and
the timing of the sale is by the end of June 1999, total capital spending for
1999 is projected to be about $220 million.

Cyprus Amax expects to spend approximately $130 million for reclamation,
remediation, and environmental compliance for the full year 1999.  If the sale
of the Coal Company does occur and the timing of the sale is by the end of June
1999, Cyprus Amax would expect to spend approximately $115 million.

During 1999 Cyprus Amax expects to be able to generate sufficient funds for
general corporate purposes, working capital needs and capital expenditures from
cash flows from operations, 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.  On February 11, 1999, the Board
of Directors announced a reduction in dividends to $0.05 per common share per
quarter effective in the second quarter of 1999.  The Board's decision was a
direct reflection of the continued weakness in copper prices.  At March 31,
1999, 90,453,579 shares of the Company's common stock were outstanding.

On August 28, 1998, the Cyprus Amax Board of Directors approved a program to buy
up to 10 million of its common shares on the open market.  As of May 13, 1999,
1,510,300 shares have been purchased at an average cost of $10.74 per share or
$16 million.  No repurchases were made during the first quarter of 1999.

Statement of Financial Accounting Standards (SFAS) No. 133, Accounting for
Derivative Instruments and Hedging Activities, was issued in June 1998.  SFAS
No. 133 requires companies to report the fair-market value of derivatives on the
balance sheet and record in income and other comprehensive income, as
appropriate, any changes in the fair value of the derivative.  This statement is
effective for all fiscal quarters of the fiscal years beginning after June 15,
1999.  The Company does not expect the statement to have a material impact on
its financial position or results of operations.

                                      -16-
<PAGE>
 
Year 2000 Conversion

State of Readiness

Cyprus Amax has created and staffed a Year 2000 (Y2K) Program Management Office
to oversee and coordinate Year 2000 conversion for the Company.  This is a
company-wide project to address the issues that are likely to arise if computer
programs and embedded computer chips are unable to properly recognize,
communicate, or react to dates in and after the Year 2000.  The Year 2000
project is a priority within Cyprus Amax, and each major business unit --
Copper/Molybdenum, Coal, and Corporate -- has dedicated full-time individuals
along with a much larger group of mine site individuals who have been assigned
specific Year 2000 responsibilities.  In certain cases, Cyprus Amax has engaged
third parties to assist in the Y2K efforts.  Year 2000 date processing has
potential implications to Cyprus Amax's business applications and automated mine
operations, such as process controllers and other electronic measuring devices.
The project is focused in three main areas:

1.  Information Technology (IT) hardware and software;

2.  Non-IT systems embedded in equipment that controls, supports, or monitors
    Cyprus Amax's assets such as mining, milling, safety, environmental,
    transportation, and communication; and

3.  Business relationships with third parties such as suppliers, customers, and
    governmental entities.

Project work dealing with IT and Non-IT systems is organized into five major
phases:

1.  Awareness      Identification and training of those responsible for timely
                   resolution of the Y2K problem.

2.  Inventory      All systems that might cause Y2K failure are identified
                   (including those linked to third parties).

3.  Assessment     Inventoried systems are classified by several levels of
                   criticality, and the state of Year 2000 compliance is
                   determined. Judgments are made as to which systems would
                   likely be materially important. Strategies and remediation
                   plans are produced.

4.  Remediation    Non-compliant systems are retired, remediated/upgraded, or
    and Testing    replaced, as appropriate,  and then tested. Based on 
                   findings, contingency plans are created and tested, if 
                   critical.

5.  Implementation Implementing the strategies and executing the plans.

Cyprus Amax has completed the awareness and inventory phases and has largely
completed the assessment phase of the project with respect to IT and Non-IT
systems.  The remediation and implementation phases involve remediating and
testing non-compliant code, replacement and testing of computing infrastructure
and telecommunications devices, and upgrading and testing of end user
applications.  These phases are in process with some major components already
fully implemented.  Cyprus Amax expects to be completed with mission-critical
systems by the end of the third quarter of 1999.

Project work dealing with external agents such as vendors and customers is
organized into four major phases:

1.  Awareness      The identification of Cyprus Amax's relationships with
                   external agents and the establishment of criticality for
                   each. Communication with each entity to elicit information
                   about their plans and actions to achieve timely Year 2000
                   readiness.

2.  Evaluation     Information from the contact is evaluated and action plans
                   are formulated as appropriate.

                                      -17-
<PAGE>
 
3.  Follow-up      Continued contact with the external agents to assure they
                   will achieve timely Year 2000 compliance and to verify our
                   reliance on current information.

4.  Mitigation/    Depending on the findings, Cyprus Amax defines alternatives 
    Contingency    and creates contingency plans.
 

Cyprus Amax has completed the awareness phase and has largely completed the
evaluation step for external entities with most work now being focused on
providing most-current compliance information to Y2K teams. The follow-up and
contingency phases have been undertaken and will be continuous and ongoing
through the end of 1999; however, the majority of the work will be completed by
the end of the second quarter of 1999.

Costs

Cyprus Amax estimates that the cost of efforts to prepare for Year 2000 from
calendar year 1997 through 1999 is from $23 million to $29 million, of which $15
million has been spent through March 31, 1999.  All project costs are being
funded with cash flows from operations.  As a result of the project, certain IT
projects to improve business functionality have been reprioritized and
accelerated.  The deferral of any IT work due to the Year 2000 efforts will not
have a material adverse effect on Cyprus Amax's results of operations or
financial condition.

Risks and Contingency Plans

Risks to Cyprus Amax resulting from failure of its systems or from failure of
third parties are essentially the same as for other firms in the mining
industry.  The following are representative of the types of risks that could
result in the event of one or more major failures of Cyprus Amax's information
systems, mining sites, or facilities to be Year 2000 ready, or similar major
failures by one or more major third party suppliers or customers of Cyprus Amax.

1.  Information systems - could include disruptions of business and transaction
    processing such as customer billing, payroll, accounts payable, purchasing,
    and other information processes until the systems can be remedied or
    replaced;

2.  Mining facilities - could include disruptions of mining processes and
    facilities with delays in delivery of products until non-compliant
    components can be remedied;

3.  Major suppliers - could include disruptions in the provision of supplies and
    components that could cause subsequent interruptions of mining activities
    and delays in delivery; and

4.  Major customers - could include disruptions in sales, revenue, and cash
    inflow as a major customer may not be Year 2000 compliant or one of their
    suppliers may experience failures that could impact the amount of copper,
    molybdenum, or coal they require.

To minimize the risks associated with the Year 2000 issue, Cyprus Amax has begun
work (1) to identify scenarios involving possible failures for Year 2000
focusing on critical systems and critical third party vendors and customers and
(2) to develop contingency plans for mitigating the impact of these scenarios.
This involves determining the most reasonably likely worst case Year 2000
scenarios.  This work is in process; however, Cyprus Amax believes that its
largest potential risks involve third parties since Cyprus Amax cannot control
their Y2K efforts.  Although there are many areas of potential risk, at present
Cyprus Amax believes that the highest potential risks are problems with the
provision of power to its operations, transportation-related problems, and the
potential failure or undue degradation of customer demand or markets for its
products, any of which could have an adverse impact on the Company's operations
and financial results.  The Company expects to have a contingency plan in place
by the third quarter of 1999.

Cyprus Amax believes it is taking the necessary steps to resolve Year 2000
issues; however, there can be no assurance that any one or more such failures
would not have a material adverse effect on Cyprus Amax. 

                                      -18-
<PAGE>
 
Actual outcomes and results could be affected by future factors including, but
not limited to, availability of skilled personnel, ability to identify and
remediate software problems, critical suppliers and subcontractors meeting
commitments, and timely actions by customers and suppliers.

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 Year 2000 compliance issues,
projections of mineral production levels, cash operating costs, capital
expenditure levels, certain significant costs 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, availability of skilled personnel, ability to identify and remediate
Year 2000 problems, impact of Year 2000 compliance problems of third parties,
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.
The Company disclaims any obligation or intention to update or revise any
forward-looking statements, whether as a result of new information, future
events or otherwise.

                                      -19-
<PAGE>
 
PART II--OTHER INFORMATION
--------------------------

Item 1.  Legal Proceedings
--------------------------

See Note 4 to Consolidated Financial Statements.

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

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, 1999.

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

(c) Set forth below are the votes cast for the election of Directors:

<TABLE>
<CAPTION>
                                            For                Withheld
                                    --------------------  -------------------
 
<S>                                 <C>                   <C>
Linda G. Alvarado                       77,575,856            2,540,065
George S. Ansell                        77,586,930            2,528,991
Rockwell A. Schnabel                    77,565,802            2,550,119
</TABLE>

    The shareholders voted to approve the appointment of PricewaterhouseCoopers
    LLP as Independent Accountants. Votes cast in favor were 78,504,442, against
    were 1,273,742, and abstaining were 337,737.

    The shareholders voted down the shareholder proposal relating to an
    Independent Nominating Committee.  Votes cast in favor were 23,108,565,
    against were 40,154,329, abstaining were 3,871,036, and non votes were
    12,981,991.

 
(d) Not applicable.
 
Item 5.  Other Information
----------------------------
Not applicable.

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
    -------      -----------------------------------------------
     (10)        Stock Purchase and Sale Agreement, dated May 12,
                 1999, by and among Cyprus Amax Minerals Company,
                 Amax Energy Inc., Cyprus Amax Coal Company and
                 RAG International Mining GmbH.
     (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,
    1999.

                                      -20-
<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, 1999                    /s/   John Taraba
       -----------------                --------------------------------
                                                  John Taraba
                                        Vice President and Controller
                                        (Principal Accounting Officer)

                                      -21-