A three-judge panel of the 6th U.S. Circuit Court of Appeals in Cincinnati will consider arguments in the cases Wednesday.
The cases pit states' rights and traditional, conservative values against what plaintiffs' attorneys say is a fundamental right to marry under the U.S. Constitution.
Since the U.S. Supreme Court struck down part of the federal Defense of Marriage Act last year, gay marriage advocates have won more than 20 victories in federal courts.
No decision has gone the other way in that time. Observers say the 6th Circuit panel could be the first to deliver a victory to gay marriage opponents.