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

                                    Form 6-K

                        REPORT OF FOREIGN PRIVATE ISSUER

                        PURSUANT TO RULE 13a-16 OR 15d-16
                     OF THE SECURITIES EXCHANGE ACT OF 1934

For the month of May 2004

Commission File Number:  0-30628


                                  ALVARION LTD.
 ------------------------------------------------------------------------------
                 (Translation of registrant's name into English)

                   21A Habarzel Street, Tel Aviv 69710, Israel
 ------------------------------------------------------------------------------
                     (Address of principal executive office)

Indicate by check mark whether the registrant files or will file annual reports
under cover of Form 20-F or Form 40-F.
Form 20-F |X|   Form 40-F |_|

Indicate by check mark if the registrant is submitting the Form 6-K in paper
as permitted by Regulation S-T Rule 101(b)(1): ____

Indicate by check mark if the registrant is submitting the Form 6-K in paper
as permitted by Regulation S-T Rule 101(b)(7): ____


Indicate by check mark whether by furnishing the information contained in this
Form, the registrant is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.
Yes |_| No |X|

If "Yes" is marked, indicate below the file number assigned to the registrant
in connection with Rule 12g3-2(b): 82-___________




The following are included in this report on Form 6-K:

                                                               Sequential
        Exhibit                Description                     Page Number
        -------                -----------                     -----------

          1.         Press release, dated May 10, 2004              3




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                                   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.


                                          ALVARION LTD.



Date: May 10, 2004                        By: /s/ Dafna Gruber
                                             ----------------------------
                                          Name:  Dafna Gruber
                                          Title: Chief Financial Officer




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                                                                       EXHIBIT 1



         Maryland County Introduces Region-Wide Carrier-Class Community
                                Broadband Network

                                   - - - - - -

             Large Municipal Wireless Broadband Deployment Leverages
             Alvarion's BreezeACCESSTM for Critical Telecom Services




Tel Aviv, Israel and Carlsbad, California, May 10, 2004 - Alvarion, the leading
provider of wireless broadband solutions worldwide, announced today that its
BreezeACCESS(TM) Complete Spectrum Point-to-Multipoint (PtMP) solution is being
implemented to expand broadband access services to county residents and
businesses in one of the nation's largest municipal deployment of wireless
broadband. The existing network, AllCoNet 1-- Allegany County (Maryland)
network--connects non-profits and public offices, including civic offices,
libraries, schools, and public safety agencies in the county. According to the
county, the expansion phase, now under construction and known as AllCoNet 2, is
planned to deliver broadband availability to 85 percent of county residences, 95
percent of businesses, and 100 percent of industrial parks, covering more than
550 square miles. The AllCoNet 2 project is valued at approximately $1million.

"Not unlike the shift from telco phone lines to PBXs in the 80s and 90s, today
forward-thinking enterprise and quasi-enterprises such as municipal governments
are leading a new trend in telecom," said Lindsay Schroth, broadband access
technologies analyst with Yankee Group. "Allegany County is one of a growing
number of municipalities that have realized substantial cost savings and service
improvements by installing their own telecom network using broadband wireless
access. The AllCoNet 2 deployment in Allegany County now represents one of the
most extensive municipal wireless broadband networks in the country, and perhaps
in the world, and one that serves as a model for other municipalities and
enterprises." Allegany County concluded that its economic future depends heavily
on the ability to offer business and residential users carrier-class broadband
services. Unsatisfied by the spotty and slow pace of private carrier broadband
deployments and facing the prospect of investing millions of dollars to deploy
fiber, the county sought alternative solutions. Spearheaded by county networking
supervisor Jeff Blank, civic leaders formed AllCoNet as a self-operated
municipal carrier to deploy wireless broadband solutions using both 6 GHz
licensed frequency bands for a Point-to-Point ring around the network as well as
unlicensed frequency bands


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Allegany County in Maryland Deploys Nation's Largest Municipal BWA Network


for Point-to-Multipoint to offer reliable, cost-effective broadband connections.
Once completed, the county will grant local ISPs wholesale access to the network
to provide services to the county's residences and businesses.

"Even if the local exchange carrier had decided to lay enough fiber for
complete, county-wide coverage, the $189 million price tag was well beyond our
means," said Blank. "While fiber would have provided more capacity, with the
Alvarion solution we were able to deploy the same carrier grade of access
services as we could with fiber, but at a fraction of the cost. Since we act as
our own carrier, there are no local fees to pay so our ISP partners will enjoy
access to the network at wholesale prices. Leveraging Alvarion's
state-of-the-art technologies, which form their BreezeACCESS Complete Spectrum
solution, we've achieved near complete coverage of our rural, and mountainous
county--something we would have waited years to get with fiber even if we had
had the financial resources to deploy it."

Alvarion's BreezeACCESS Complete Spectrum solution uses multiple frequency bands
and forms the core of the county's last mile wireless broadband network. The
Alvarion solution was chosen for AllCoNet 2 because of its success as part of
the original AllCoNet deployment, in which leased lines for public buildings
have been replaced with wireless connections.

"Like numerous other rural communities throughout North America, the people of
Allegany County faced overwhelming financial and logistical challenges when
contemplating the deployment of critical broadband services using fiber or other
wireline methods," added Amir Rosenzweig, President of Alvarion, Inc. "The
vision that Allegany County leaders realized that by employing a wireless
solution with the same reliability, security, and quality of service
capabilities as wired technologies, they could become their own carrier, and
take control of their broadband future. And even better, wireless broadband gave
them the ability to do it much faster and at a dramatically lower cost than is
possible by any other means."

                                       ###

About AllCoNet
AllCoNet is the Intranet for Allegany County, Maryland. Consisting of a
partnership of government and non-profit entities, AllCoNet is a creative and
innovative approach to meeting the information needs of local schools,
government agencies, and communities. AllCoNet is committed to being
self-servicing, and dedicated to employing the newest available technology to
improve service, while containing costs. The AllCoNet Infrastructure is an
IP-based high speed Intranet providing the security of a world-class firewall
and the stability and speed of a fully monitored microwave network. AllCoNet
provides a virtually unlimited IP space and any and all Internet services
including DNS/RDNS, SLAPD, POP/IMAP, NNTP and hosting.

AllCoNet 2 is the second inception for the AllCoNet partners which allows
AllCoNet to interface with the private sector. AllCoNet 2 supplies Allegany
County's public and private sectors with an infrastructure that


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provides last mile connectivity for local facilities to tier one providers and
local ISPs at lower costs than traditional local loop technologies. AllCoNet 2's
objectives include expanding broadband/wideband telecommunications services to
attract high-tech and bio-tech businesses, improving the telecommunications
infrastructure of Allegany County to bridge the digital divide, and providing
telecommunication options for business start-ups and incubators.



About Alvarion
With over 1.5 million units deployed in 130 countries, Alvarion is the worldwide
leader in wireless broadband providing systems to carriers, ISPs and private
network operators. Featuring the industry's most extensive portfolio and
covering the full range of frequency bands, the company's products enable the
delivery of business and residential broadband access, corporate VPNs, mobile
base station feeding, Hotspot coverage extension, community interconnection, and
public safety communications. Alvarion works with several leading OEM providers
and through over 200 local partners to support its diverse customer base in
solving their last mile connection challenges wherever located.

As an industry pioneer, Alvarion has been driving and delivering wireless
broadband innovations for 10 years from core technology developments to creating
and promoting industry standards. Most recently offering OFDM-based systems and
taking leading roles in the IEEE and HiperMAN standards, the company's prominent
work in the WiMAX ForumTM is focused on leading the wireless broadband market to
widespread adoption of standards-based products.

For more information, visit Alvarion's World Wide Web site at www.alvarion.com

This press release contains forward -looking statements within the meaning of
the "safe harbor" provisions of the Private Securities Litigation Reform Act of
1995. These statements are based on the current expectations or beliefs of
Alvarion's management and are subject to a number of factors and uncertainties
that could cause actual results to differ materially from those described in the
forward -looking statements. The following factors, among others, could cause
actual results to differ materially from those described in the forward-looking
statements: inability to further identify, develop and achieve success for new
products, services and technologies; increased competition and its effect on
pricing, spending, third-party relationships and revenues; as well as the in
ability to establish and maintain relationships with commerce, advertising,
marketing, and technology providers and other risks detailed from time to time
in filings with the Securities and Exchange Commission.

Information set forth in this press release pertaining to third parties has not
been independently verified by Alvarion and is based solely on publicly
available information or on information provided to Alvarion by such third
parties for inclusion in this press release. The web sites appearing in this
press release are not and will not be included or incorporated by reference in
any filing made by Alvarion with the Securities and Exchange Commission, which
this press release will be a part of.

You may request Alvarion's future press releases or a complete Investor Kit by
contacting Carmen Deville, Investor Relations: carmen.deville@alvarion.com or
760-517-3188.



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