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DALLAS -- A Texas state appeals court is scheduled to hear arguments Wednesday in the case of a gay couple in Dallas that was granted a divorce even though the state doesn't recognize same-sex marriage.

Texas Attorney General Greg Abbott is appealing the lower court judge's ruling on the grounds that protecting the "traditional definition of marriage" means doing the same for divorce.

In 2005, Texas voters passed a constitutional ban on same-sex marriage by a 3-to-1 margin even though state law already prohibited it. As a result, the state of Texas says a union granted in a state where same-sex marriage is legal can't be dissolved with a divorce in a state where it's not.

Abbott is also appealing a similar case in Austin, where a couple who married in Massachusetts in 2004, was granted a divorce by a judge who ruled that the same-sex marriage ban violates equal rights guaranteed by the U.S. Constitution.

The Dallas couple, who married in 2006 in Massachusetts and separated two years later, simply want an official divorce, said Peter Schulte, the attorney for one of the men, who is known only as J.B.

J.B. and partner H.B had an amicable separation, with no disputes on separation of property and no children involved, Schulte said.

Angelique Naylor, who was granted a divorce from Sabina Daly. a woman with whom she adopted a child, says she didn't file in the Austin court as an equal rights statement -- she just wants to get on with her life.

"We didn't ask for a marriage; we simply asked for the courtesy of divorce," said Naylor.

In 2004, Massachusetts became the first state to let same-sex couples tie the knot. Now, Connecticut, Iowa, New Hampshire, Vermont and the District of Columbia also allow them. But gay and lesbian couples who turn to the courts when they break up are getting mixed results across the nation.

A Pennsylvania judge last month refused to divorce two women who married in Massachusetts, while New York grants such divorces even though the state doesn't allow same-sex marriage.

"The bottom line is that same-sex couples have families and their families have the same needs and problems, but often don't have the same rights," said Jennifer Pizer, a lawyer for Lambda Legal, a national legal organization that promotes equal rights for gay, lesbian, bisexual and transgender people.

"It really is an unenviable position that the courts have put these couples in," said Karen Loewy, an attorney at the Gay and Lesbian Advocates and Defenders.

Abbott, a Republican seeking re-election, argued in court filings that because the state doesn't recognize gay marriage there can be no divorce, but a gay couple can have a marriage voided.

Attorneys representing such couples argue that voiding a marriage here could leave it intact in other states, creating problems for property divisions and other issues.

"OK, you're recommending voidance, but how does that work?" asked Jennifer Cochran, Naylor's attorney. "Is it only void in Texas and can you void a marriage that's valid in another state? The attorney general I feel didn't answer those questions."

Kelly Shackelford, chief counsel for the conservative Liberty Institute in Plano, called the judge's decision "outrageous judicial activism." The institute has filed a friend of the court brief to the appeals court on behalf of the two Republican state lawmakers who co-sponsored the amendment banning gay marriage: state Rep. Warren Chisum and former state Sen. Todd Staples.

"It's a backdoor run at establishing same-sex so-called marriage against the people's vote," Shackelford said. "Once you grant the divorce, you are recognizing that there was a marriage."

Dallas divorce attorney Tom Greenwald said he's advising gay couples to wait and see how things play out in the courts.

"Getting the court of appeals to even accept the issue is a step in the right direction in getting some clarity on this," he said. "We just don't know how to treat it."

Naylor and Daly, who've been separated since 2007, toyed with the idea of one of them moving to a state where gay marriage is legal until a divorce is finalized, but that didn't seem practical.

Naylor said that eventually, she and Daly, who had real estate-related businesses and renovated homes, worked out a custody arrangement for their now 4 1/2-year-old son. Naylor said that when she heard about the Dallas divorce, she thought it was worth a try and filed for her own, even though several attorneys she spoke with weren't so sure.

"They said it's too up in the air, wait and see for appeals," Naylor said. "I didn't have a lot of time to wait and see."

The Associated Press contributed to this report.