But the Texas Attorney General's Office argued before the three-judge panel that the marriage isn't recognized by Texas, so they cannot get a divorce. Jimmy Blacklock, an assistant Texas solicitor general, said the men's union can only be voided.
"The parties lack standing to file a divorce case because they're not married," he said.
The Dallas men wed in 2006 in Massachusetts, where gay marriage is legal, and separated two years later.
Jody Scheske, who represents the man listed in court records only as J.B., said his client doesn't want to overturn the state's marriage ban, but only wants to end his own marriage.
"He is not seeking to enter into a same-sex marriage; he's seeking to end a marriage that was valid," Scheske said.
Attorney General Greg Abbott appealed a Dallas state district judge's ruling in October that granted a divorce to the men and said the state's same-sex marriage ban violates equal rights guaranteed by the Constitution.
Blacklock said the state's ban on gay marriage doesn't violate the Constitution.
Abbott is also appealing an Austin judge's ruling this spring that granted a divorce to two women married in Massachusetts.