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                                                                   EXHIBIT 5,8.1
 
                    [LETTERHEAD OF APPLEBY SPURLING & KEMPE]
 
                                                                   30 March 1999
 
Loral Space & Communications Limited
600 Third Avenue
New York
NY 10016
 
Ladies and Gentlemen
 
     We have acted as Bermuda counsel for Loral Space & Communications Limited,
a Bermuda company, (the "Company"), in connection with the filing by the Company
with the Securities and Exchange Commission (the "Commission") of a registration
statement (the "Registration Statement") on Form S-4 under the Securities Act of
1933, as amended (the "Securities Act") relating to the proposed issuance, in
exchange for $350,000,000 aggregate principal amount of the Company's 9 1/2%
Senior Notes due 2006 (the "Old Notes"), of $350,000,000 aggregate principal
amount of the Company's 9 1/2% Notes due 2006 (the "New Notes", and collectively
with the Old Notes, the "Notes"). The New Notes are to be issued pursuant to an
indenture dated as of 15 January 1999 (the "Indenture"), between the Company and
The Bank of New York, as trustee (the "Trustee"). Capitalized terms used herein
and not otherwise defined herein have the meanings ascribed thereto in the
Indenture.
 
     In so acting, we have examined originals or copies, certified or otherwise
identified to our satisfaction, of the Registration Statement and such corporate
records, agreements, documents and other instruments, as we have deemed
necessary for the purpose of this opinion, and we have relied on statements and
certificates of officers and representatives of the Company and public
officials.
 
     We have assumed:
 
     (i)   the truth, accuracy and completeness as the date hereof of all
           representations as to factual matters made in the documents which we
           have examined;
 
     (ii)   the genuineness of all signatures on the documents which we have
            examined; and
 
     (iii)  The conformity to original documents of all documents produced to us
            as copies and the authenticity of all original documents which, or
            copies of which, have been submitted to us.
 
     Based upon and subject to the foregoing and subject to the reservations
mentioned below and to any matters not disclosed to us, we are of the opinion
that:
 
     (i)    the Company is an exempted company duly incorporated and validly
            existing under Bermuda law and is in good standing under the laws of
            Bermuda;
 
     (ii)   the Company has full power and authority, and has obtained all
            Bermuda governmental authorisations, licenses, permits, certificates
            and approvals as are necessary to own its properties and to conduct
            its business as described in the Registration Statement;
 
     (iii)   all the Shares have been duly and validly authorised, issued, fully
             paid and non-assessable; and
 
     (iv)   the legal conclusions set forth in the discussion of Bermuda tax law
            under the headings "Foreign Issuer Considerations -- Bermuda Tax
            Considerations" and "The Exchange Offer"
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            are our opinions, and it is our opinion that this discussion
            addresses the material Bermuda tax consequences of an investment in
            the Notes.
 
     Our reservations are as follows:
 
(A)   We express no opinion as to any law other than Bermuda law and none of the
      opinions expressed herein relates to compliance with or matters governed
      by the laws of any jurisdiction other than Bermuda. Where an obligation is
      to be performed in a jurisdiction other than Bermuda, a Bermuda court may
      decline to enforce it to the extent that such performance would be illegal
      or contrary to public policy under the laws of such other jurisdiction.
 
(B)   We express no opinion as to the availability of equitable remedies, such
      as specific performance or injunctive relief, or as to any matters which
      are within the discretion of the Bermuda courts, such as the award of
      costs or questions related to jurisdiction. Further, we express no opinion
      as to the validity or binding effect in Bermuda of any waiver of or
      obligation to waive any provision of law (whether substantive or
      procedural) or any right or remedy arising through circumstances not known
      at the time of the filing of the Registration Statement.
 
(C)   Section 9 of the Interest and Credit Charges (Regulation) Act, 1975
      provides that the Bermuda courts have discretion as to the amount of
      interest if any payable on the amount of a judgment after date of
      judgment. If the court does not exercise that discretion, then interest
      will accrue at the statutory rate which is currently seven per cent per
      annum.
 
(D)   Where a party is vested with a discretion or may determine a matter in its
      opinion, such discretion may have to be exercised reasonably or such an
      opinion may have to be based on reasonable grounds.
 
(E)   For the purposes of this opinion:
 
        (a)  the term "fully paid" means, in relation to the issued shares of a
             company limited by shares (that is to say, a company having the
             liability of its members limited by its Memorandum of Association
             to the amount, if any, unpaid on the shares held by them), that
             members holding such shares have no liability to make any
             contribution or other payment to the company in respect of those
             shares; and
 
        (b)  the term "non-assessable" means, in relation to fully-paid shares
             of a company, that such member shall not be bound by an alteration
             to the Memorandum of Association or to the Bye-laws of that company
             after the date upon which he became a member, if and so far as the
             alteration requires him to take, or subscribe for additional
             shares, or in any way increases his liability to contribute to the
             share capital of, or otherwise to, pay money to the company.
 
     This opinion is issued on the basis that it will be construed in accordance
with the provisions of Bermuda law.
 
     We hereby consent to the filing of this opinion as an exhibit to the
Registration Statement and to the reference to us in the Prospectus included as
part of the Registration Statement. In giving such consent, we do not admit
hereby that we come within the category of persons whose consent is required
under Section 7 of the Securities Act, or the Rules and Regulations of the
Securities and Exchange Commission thereunder.
 
                                          Yours faithfully
 
                                          /s/ APPLEBY SPURLING & KEMPE
 
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