Another way of saying it, and the one I use. It's also nice to use one word if you can. More hits on Google. See any of a number of cases of the OHIM Opposition Division :)

Depende. Si la otra parte es la que se opone al registro de la marca, puedes usar "opposing" o "contesting". Si simplemente es la parte contraria, con poner "the other party" se entiende.

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Note added at 8 hrs (2008-02-13 14:15:44 GMT)
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Quiero hacer notar, que si bien en español "contraparte" es el oponente, en inglés "counterparty" tiene una connotación más bien exclusivamente financiera.

counterparty

coun·ter·par·ty [kówntər prtee]
(plural coun·ter·par·ties)
noun
finance other participant in business transaction: one of the two people, companies, or organizations involved in a transaction, as referred to by the other participant in the transaction

Microsoft® Encarta® Reference Library 2005. © 1993-2004 Microsoft Corporation. All rights reserved.

Merriam-Webster's Collegiate 11th ed.
Main Entry:coun£ter£par£ty
Pronunciation:-*p*r-t*
Function:noun
Date:1980

: a party to a financial transaction

http://www.answers.com/counterparty?cat=biz-fin
The other party that participates in a financial transaction. Every transaction must have a counterparty in order for the transaction to go through. More specifically, every buyer of an asset must be paired up with a seller that is willing to sell and vice versa.

Investopedia Says:
All trades require some sort of counterparty. For example, the counterparty to the option buyer would be the option writer. One of the risks involved in any transaction is counterparty risk, which is the risk that the counterparty will be unable to fulfill his or her duties.