<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D. C. 20549

                                 ---------------

                                    FORM 10-Q

[X]     QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE 
        SECURITIES EXCHANGE ACT OF 1934

                  For the quarterly period ended March 29, 1998

                                       OR

[ ]     TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE 
        SECURITIES EXCHANGE ACT OF 1934

           For the transition period from _____________to_____________

                                 ---------------

                          Commission File Number 0-9653

                                   XICOR, INC.
             (Exact name of registrant as specified in its charter)

               California                              94-2526781
     (State or other jurisdiction of                 (I.R.S.Employer
     incorporation or organization)                Identification No.)

 1511 Buckeye Drive, Milpitas, California                 95035
 (Address of principal executive offices)              (Zip Code)

       Registrant's telephone number, including area code: (408) 432-8888

         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 OUTSTANDING AT MARCH 29, 1998
                                   19,097,852

<PAGE>   2

                                   XICOR, INC.

                                    FORM 10-Q

                          QUARTER ENDED MARCH 29, 1998


                                      INDEX


<TABLE>
<CAPTION>
                                                                                     PAGE
                                                                                     ----
<S>         <C>                                                                      <C>
PART I:     FINANCIAL INFORMATION

            ITEM 1.    FINANCIAL STATEMENTS

                       Consolidated Balance Sheets at March 29, 1998                   1
                       and December 31, 1997

                       Consolidated Statements of Operations for the three             2
                       months ended March 29, 1998 and March 30, 1997

                       Consolidated Statements of Cash Flows for the three             3
                       months ended March 29, 1998 and March 30, 1997

                       Notes to Consolidated Financial Information                     4

            ITEM 2.    MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL               5
                       CONDITION AND RESULTS OF OPERATIONS


PART II:    OTHER INFORMATION

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

SIGNATURES                                                                             8
</TABLE>


                                       -i-

<PAGE>   3

PART I: FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS

                                   XICOR, INC.
                           CONSOLIDATED BALANCE SHEETS

                                     ASSETS

<TABLE>
<CAPTION>
                                                      March 29,     December 31,
                                                        1998           1997
                                                    ------------    ------------
                                                     (Unaudited)
<S>                                                 <C>             <C>           
Current assets:
  Cash and cash equivalents                         $ 16,835,000    $ 21,106,000
  Short-term investments                               8,413,000      11,372,000
  Accounts receivable                                 10,788,000      11,003,000
  Inventories                                         25,387,000      23,933,000
  Prepaid expenses and other current assets              954,000       1,013,000
                                                    ------------    ------------
       Total current assets                           62,377,000      68,427,000

Property, plant and equipment,
  at cost less accumulated depreciation               45,773,000      46,628,000
Other assets                                             207,000         206,000
                                                    ------------    ------------
                                                    $108,357,000    $115,261,000
                                                    ============    ============

                      LIABILITIES AND SHAREHOLDERS' EQUITY

Current liabilities:
  Accounts payable                                  $ 10,997,000    $ 11,596,000
  Accrued expenses                                     8,051,000       8,133,000
  Deferred income on shipments to distributors        11,089,000      13,913,000
  Current portion of long-term obligations             6,753,000       6,537,000
                                                    ------------    ------------
       Total current liabilities                      36,890,000      40,179,000
                                                    ------------    ------------
Long-term obligations                                 17,704,000      18,974,000
                                                    ------------    ------------

Shareholders' equity:
  Preferred stock; 5,000,000 shares authorized                --              --
  Common stock; 75,000,000 shares authorized;
    19,097,852 and 19,091,727 shares outstanding     124,213,000     124,204,000
  Accumulated deficit                                (70,450,000)    (68,096,000)
                                                    ------------    ------------
                                                      53,763,000      56,108,000
                                                    ------------    ------------
                                                    $108,357,000    $115,261,000
                                                    ============    ============
</TABLE>


          See accompanying notes to consolidated financial information


                                       -1-

<PAGE>   4

                                   XICOR, INC.
                      CONSOLIDATED STATEMENTS OF OPERATIONS
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                      Three Months Ended
                                             -----------------------------------
                                             March 29, 1998       March 30, 1997
                                             --------------       --------------
<S>                                          <C>                  <C>         
Net sales                                     $27,746,000         $29,513,000
Cost of sales                                  19,892,000          17,718,000
                                              -----------         -----------
  Gross profit                                  7,854,000          11,795,000
                                              -----------         -----------
Operating expenses:
  Research and development                      4,566,000           4,613,000
  Selling, general and administrative           5,498,000           5,158,000
                                              -----------         -----------
                                               10,064,000           9,771,000
                                              -----------         -----------
Income (loss) from operations                  (2,210,000)          2,024,000
Interest expense                                 (500,000)           (410,000)
Interest income                                   356,000             502,000
                                              -----------         -----------
Income (loss) before income taxes              (2,354,000)          2,116,000
Provision for income taxes                             --             106,000
                                              -----------         -----------
Net income (loss)                             $(2,354,000)        $ 2,010,000
                                              ===========         ===========
Net income (loss) per common share:
     Basic                                    $     (0.12)        $      0.11
                                              ===========         ===========
     Diluted                                  $     (0.12)        $      0.10
                                              ===========         ===========
Shares used in per share calculations:
     Basic                                     19,095,000          18,888,000
                                              ===========         ===========
     Diluted                                   19,095,000          19,683,000
                                              ===========         ===========
</TABLE>


          See accompanying notes to consolidated financial information


                                       -2-

<PAGE>   5

                                   XICOR, INC.
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                                           Three Months Ended
                                                                   -----------------------------------
                                                                   March 29, 1998       March 30, 1997
                                                                   --------------       --------------
<S>                                                                  <C>                  <C>
Cash flows from operating activities:
  Net income (loss)                                                  $(2,354,000)         $ 2,010,000
  Adjustments to reconcile net income to
    cash provided by operating activities:
      Depreciation and amortization                                    2,977,000            2,669,000
      Changes in assets and liabilities:
        Accounts receivable                                              215,000           (1,497,000)
        Inventories                                                   (1,454,000)          (2,847,000)
        Prepaid expenses and other current assets                         59,000              230,000
        Other assets                                                      (1,000)              31,000
        Accounts payable and accrued expenses                           (681,000)             722,000
        Deferred income on shipments to distributors                  (2,824,000)             945,000
                                                                     -----------          -----------
Net cash provided by (used for) operating activities                  (4,063,000)           2,263,000
                                                                     -----------          -----------
Cash flows from investing activities:
  Investments in plant and equipment, net                             (1,679,000)          (3,643,000)
  Purchases of short-term investments                                 (1,097,000)          (6,097,000)
  Maturities of short-term investments                                 4,056,000            9,283,000
                                                                     -----------          -----------
Net cash provided by (used for) investing activities                   1,280,000             (457,000)
                                                                     -----------          -----------
Cash flows from financing activities:
  Repayments of long-term obligations                                 (1,497,000)          (1,419,000)
  Proceeds from sale of common stock to employees                          9,000               87,000
                                                                     -----------          -----------
Net cash used for financing activities                                (1,488,000)          (1,332,000)
                                                                     -----------          -----------
Increase (decrease) in cash and cash equivalents                      (4,271,000)             474,000
Cash and cash equivalents at beginning of year                        21,106,000           20,414,000
                                                                     -----------          -----------
Cash and cash equivalents at end of quarter                          $16,835,000          $20,888,000
                                                                     ===========          ===========
Supplemental information:
Cash paid (refunded) for:
  Interest expense                                                   $   493,000          $   410,000
  Income taxes                                                          (133,000)              59,000
Equipment acquired pursuant to long-term obligations                     443,000            3,248,000
</TABLE>


          See accompanying notes to consolidated financial information


                                       -3-

<PAGE>   6

                                   XICOR, INC.
                   NOTES TO CONSOLIDATED FINANCIAL INFORMATION
                                   (Unaudited)

NOTE 1 - THE COMPANY:

         In the opinion of management, all adjustments necessary for a fair
statement of the results of the interim periods presented (consisting only of
normal recurring adjustments) have been included. These financial statements,
notes and analyses should be read in conjunction with Xicor's Annual Report on
Form 10-K for the year ended December 31, 1997 filed with the Securities and
Exchange Commission.

NOTE 2 - NET INCOME (LOSS) PER SHARE:

         Basic net income (loss) per share is computed using the weighted
average number of common shares outstanding. Diluted net income (loss) per share
is computed using the weighted average number of common shares and all dilutive
potential common shares outstanding. For the quarter ended March 29, 1998, the
number of shares used in the calculation of both earnings per share (EPS)
amounts were the same since 329,000 common stock equivalents relating to
outstanding stock options were excluded as they were antidilutive. Common stock
equivalents were the only reconciling item between the number of shares used to
calculate Basic EPS and Diluted EPS for the quarter ended March 30, 1997. At
March 29, 1998, options for 2,276,925 shares were outstanding.

NOTE 3 - BALANCE SHEET DETAIL:

<TABLE>
<CAPTION>
                                                       March 29,            December 31,
                                                         1998                   1997
                                                    --------------         --------------
<S>                                                 <C>                    <C>           
Inventories:
  Raw materials and supplies                        $    3,940,000         $    4,229,000
  Work in process                                       14,747,000             13,012,000
  Finished goods                                         6,700,000              6,692,000
                                                    --------------         --------------
                                                    $   25,387,000         $   23,933,000
                                                    ==============         ==============
Property, plant and equipment:
  Leasehold improvements                            $   17,590,000         $   17,518,000
  Equipment                                            117,518,000            116,349,000
  Furniture and fixtures                                 1,851,000              1,817,000
  Construction in progress                               7,995,000              8,104,000
                                                    --------------         --------------
                                                       144,954,000            143,788,000
  Less accumulated depreciation                        (99,181,000)           (97,160,000)
                                                    --------------         --------------
                                                    $   45,773,000         $   46,628,000
                                                    ==============         ==============
Accrued expenses:
  Accrued wages and employee benefits               $    3,835,000         $    3,984,000
  Other accrued expenses                                 4,216,000              4,149,000
                                                    --------------         --------------
                                                    $    8,051,000         $    8,133,000
                                                    ==============         ==============
</TABLE>

Accounts receivable:

         Accounts receivable at March 29, 1998 and December 31, 1997 are
presented net of an allowance for doubtful accounts of $500,000.


                                       -4-
<PAGE>   7

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

         The following discussion should be read in conjunction with the
accompanying Quarterly Financial Information and Notes thereto and Xicor's
Annual Report on Form 10-K for the year ended December 31, 1997 and is qualified
in its entirety by the foregoing. The results of operations for the quarter
ended March 29, 1998 are not necessarily indicative of results to be expected in
future periods.

RESULTS OF OPERATIONS

         Sales for the first quarter of 1998 were $27.7 million, a decrease from
first quarter 1997 sales of $29.5 million and fourth quarter 1997 sales of $31.4
million. The economic difficulties in Asia and global pricing pressures are
posing major challenges for Xicor in 1998. During the first quarter of 1998, the
Japanese and Korean economies continued to be weak, and our sales in those
countries decreased dramatically from the fourth quarter.

         Gross profit as a percentage of sales was 28% for the first quarter of
1998, compared to 40% for the comparable prior year quarter. The decline in the
gross profit percentage was primarily due to lower average selling prices as a
result of competitive price pressures and Xicor's increased manufacturing cost
level associated with increased production capacity and upgrading of the wafer
fabrication operations during 1997.

         Research and development expenses were 16% of sales in the first
quarter of both 1998 and 1997. Research and development activities require an
increasing degree of complexity of design and manufacturing process technology
and consequently more funds are expected to be invested in research and
development in 1998 than were invested in 1997.

         Selling, general and administrative expenses increased from 17% of
sales for the first quarter of 1997 to 20% of sales during the first quarter of
1998 primarily due to the lower sales level and a $162,000 bad debt write off
related to the sudden bankruptcy of an Asian customer.

         Interest expense increased in the first quarter of 1998 compared to the
first quarter of 1997 due to the financing of additional capital equipment
acquisitions during 1997.

         Interest income decreased in the first quarter of 1998 compared to the
first quarter of 1997 due to a decrease in the average balance invested caused
primarily by funds used for 1997 capital asset purchases, ongoing debt
repayments and first quarter 1998 operating activities. Interest income is
expected to decrease during the remaining 1998 quarters principally due to the
utilization of funds for operating activities, equipment purchases and
normal debt repayments.

         No taxes were provided for the first quarter of 1998 due to the net
loss. The provision for income taxes for the first quarter of 1997 consisted
primarily of federal and state minimum taxes, which result from limitations on
the use of net operating loss carryforwards, and foreign taxes. Net deferred tax
assets of $33.9 million at December 31, 1997 remain fully reserved because of
the uncertainty regarding the ultimate realization of these assets.


                                       -5-

<PAGE>   8
         The reduced sales level, together with price erosion, were the primary
causes of the first quarter 1998 loss. Additionally, Xicor's manufacturing costs
increased in the first quarter of 1998 compared to the first quarter of 1997 due
to increased production capacity and upgrading of the wafer fabrication
operations in 1997. At the beginning of the second quarter of 1998, Xicor
reduced the production volume in its factory to correspond with ongoing weak
business conditions. The resultant lower factory utilization, along with
anticipated continued weak sales and price erosion, are expected to negatively
impact second quarter 1998 results relative to the first quarter of 1998.

"SAFE HARBOR" STATEMENT UNDER THE PRIVATE SECURITIES LITIGATION REFORM ACT OF
1995

         This quarterly report contains forward-looking statements within the
meaning of Section 27A of the Securities Act of 1933 and Section 21E of the
Securities Exchange Act of 1934, including statements regarding lower factory
utilization, anticipated continued weak sales, price erosion and the negative
impact on second quarter 1998 results relative to the first quarter of 1998.
Except for historical information, the matters discussed in this quarterly
report are forward-looking statements that are subject to certain risks and
uncertainties that could cause the actual results to differ materially from
those projected. Factors that could cause actual results to differ materially
include the following: general economic conditions (including in Asia) and
conditions specific to the semiconductor industry, fluctuations in customer
demand, competitive factors such as pricing pressures on existing products and
the timing and market acceptance of new product introductions, Xicor's ability
to have available an appropriate amount of production capacity in a timely
manner, manufacturing efficiencies, the timely development of new products and
processes, and the risk factors listed from time to time in Xicor's SEC
reports, including but not limited to the "Factors Affecting Future Results"
section below and Part I, Item 1. of the Form 10-K. Readers are cautioned not
to place undue reliance on these forward-looking statements, which speak only
as of the date hereof. Xicor undertakes no obligation to publicly release or
otherwise disclose the result of any revision to these forward-looking
statements which may be made as a result of events or circumstances after the
date hereof or to reflect the occurrence of unanticipated events.

FACTORS AFFECTING FUTURE RESULTS

         The semiconductor industry is highly competitive and characterized by
rapidly changing technology and steadily declining product prices. Xicor's
results of operations are affected by a wide variety of factors, including
general economic conditions and conditions specific to the semiconductor
industry, decreases in average selling price over the life of any particular
product, the timing of new product introductions (both by Xicor and
competitors), availability of new manufacturing technologies, the ability to
secure intellectual property rights in a rapidly evolving market and the ability
to have an appropriate amount of production capacity in a timely manner. The
sales level in any specific quarter is also a function of orders received during
that quarter, as customers continue to shorten lead times for purchase
commitments. Consistent with industry practice, customer orders are generally
subject to cancellation by the customer without penalty. Xicor may be at a
disadvantage in competing with major domestic and foreign concerns that have
significant financial resources, established and diverse product lines,
worldwide vertically integrated production facilities and extensive research and
development capabilities.


                                       -6-

<PAGE>   9

         The semiconductor industry is also characterized by substantial capital
and research and development investment for products and processes. The rapid
rate of technological change within the industry requires Xicor to continually
develop new and improved products and processes to maintain its competitive
position. Xicor expects to continue to invest in the research and development of
new products and manufacturing processes in 1998 and beyond, although there can
be no assurances that such research and development efforts or new products will
be successful.

         Xicor has an investment portfolio of fixed income securities that are
classified as "held to maturity securities". These securities, like all fixed
income instruments, are subject to interest rate risk and will fall in value if
market interest rates increase. Xicor attempts to limit this exposure by
investing primarily in short-term securities.

         From time-to-time Xicor makes certain capital equipment or other
purchases denominated in foreign currencies. As a result, Xicor's cash flows and
earnings are exposed to fluctuations in interest rates and foreign currency
exchange rates. Xicor attempts to limit these exposures through operational
strategies and generally has not hedged currency exposures.

         Due to the foregoing and other factors, past results are a much less
reliable predictor of the future than is the case in many older, more stable and
less dynamic industries. In addition, the securities of many high technology
companies, including Xicor, have historically been subject to extensive price
and volume fluctuations that may adversely affect the market price of their
common stock.

LIQUIDITY AND CAPITAL RESOURCES

         At March 29, 1998, Xicor had $25.2 million in cash, cash equivalents
and short-term investments compared to $32.5 million at December 31, 1997.
During the first quarter of 1998, Xicor used $4.1 million of cash for operating
activities, $1.7 million for equipment purchases and $1.5 million to repay
long-term obligations. Xicor used long-term financing to acquire additional
capital assets of $0.4 million during the quarter ended March 29, 1998.

         Capital expenditures for the balance of 1998 are planned at
approximately $13 million, $2 million of which had been committed as of March
29, 1998. The acquisitions consist principally of equipment necessary for volume
production using its submicron technology which is in the latter stages of
development. Xicor is investigating equipment financing for a large portion of
these acquisitions, but there is no assurance that such financing will be
available.

         Xicor has a line of credit agreement with a financial institution that
expires March 31, 1999, provides for borrowings of up to $7.5 million against
eligible accounts receivable and is secured by all of Xicor's assets. Interest
on borrowings is charged at the prime lending rate plus 2% and is payable
monthly. At March 29, 1998, the entire $7.5 million was available to Xicor based
on the eligible accounts receivable balances and the borrowing formulas. To
date, no amounts have been borrowed under this line of credit. Management
believes that currently available cash and expected equipment financing will be
adequate to support Xicor's operations for the next twelve months.


                                       -7-

<PAGE>   10

PART II: OTHER INFORMATION

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

                (a)     Exhibits:

                        27      Financial Data Schedule

                (b)     Reports on Form 8-K:

                        No reports on Form 8-K were filed with the Securities
                        and Exchange Commission during the quarter ended 
                        March 29, 1998.

                                   SIGNATURES

         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.

                                       XICOR, INC., a
                                       California Corporation

                                       By /s/  Raphael Klein
                                          --------------------------------------
                                          Raphael Klein
                                          Chief Executive Officer
                                          (Principal Executive Officer)

                                       By /s/  Geraldine N. Hench
                                          --------------------------------------
                                          Geraldine N. Hench
                                          Vice President, Finance
                                          (Principal Financial Officer)

Date:  May 11, 1998


                                       -8-
<PAGE>   11
                                 EXHIBIT INDEX

<TABLE>
<CAPTION>
     Exhibit #           Description
     ---------           -----------
     <S>                 <C>
        27               Financial Data Schedule
</TABLE>