Русско-англо-русский юридический словарь

A cross-appeal is a request filed by an appellee requesting that a higher court review a decision made by a lower court. The difference between an appeal and a cross-appeal is essentially arbitrary and dependent only on who filed the request for a higher court's review first. The first party to file is called the petitioner or appellant, and its request for review is an appeal. If an opposing party (called the respondent or appellee) also wishes to request review of a lower court's decision, that request is called a cross-appeal. (law.cornell.edu)

The appellant in the new case can be either the plaintiff (or claimant), defendant, third-party intervenor, or respondent (appellee) from thelower case, depending on who was the losing party. The winning party from the lower court, however, is now the respondent. (Wikipedia)

The appellant is the party who, having lost part or all their claim in a lower court decision, is appealing to a higher court to have their case reconsidered. (Wikipedia)

The Court, having weighed the evidence and apportioned the advantage accruing from the dereliction, abrogates the appeal and all similar procedures, discharges the appellant and amends the judgement of the lower Court [...] (Art Institute Chicago)