Not for divorce cases. Rule 1.5(c)(1) of the Oregon Rules of Professional Conduct prohibits attorneys from working for a contingency fee in a domestic relations case.
Actually, I would be surprised if any attorney would take any appellate case on a purely contingent basis. There are two reasons: first, most appellate cases don't actually result in a money award, even if you win (although they might include an award for reasonable attorney fees). Rather, they're more likely to result in a new trial, with the trial court directed to consider or decide one particular issue differently.
Second, appeals are a huge amount of work, that can occupy a large part of a lawyer's time for months on end. Lawyers need to eat too.
But, as I said, there can be a provision for attorney fees if you do win on an appeal. You can consult with an attorney who specializes in domestic relations appeals to see whether the matter is worth pursuing.
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As the prior responder states there are ethical rules against taking a matrimonial case in a contingency. That should be the entire answer rather than the economics of why a lawyer would be reluctant to take an appeal on a contingency.
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Your best bet is if your case has an aiisue that could result in an award of attorney fees. However, almost no attorneys will work for the length of time an appeal takes in the hope of eventually getting an order awarding fees.
This answer does not create an attorney-client relationship. It is advisable to consult with an attorney with full disclosure of relevant facts for a comprehensive leagl opinion.