The Texas Supreme Court is hearing a case that conservatives hope can lead to an overturning of legalised gay marriage nationwide.
Opponents are suing the city of Houston over its decision to extend benefits to same-sex spouses of city employees.
Houston officials argue that they are required to provide them under a US Supreme Court 2015 ruling that same-sex marriage is a legal right nationally.
The court had initially chosen not to hear the legal challenge.
However, under pressure from Republican state lawmakers, including Governor Greg Abbot, the all-Republican court reversed that decision in January and allowed the trial to begin.
In several amicus briefs (advisory opinions to the court), lawmakers asked the court to reject the "'ideology of the sexual revolution" that federal judges had passed into law.
Conservative lawyers argue that the 2015 decision by the US Supreme Court in Washington, Obergefell v Hodges, does not contain language specifically extending benefits to gay spouses.
"Obergefell may require states to license and recognize same-sex marriages, but that does not require states to give taxpayer subsidies to same-sex couples," lawyers challenging Houston policy wrote in a court filing.
Houston officials say they had no choice but to offer the benefits, since the law requires same-sex married couples to be extended the same rights as heterosexual married couples.
Arguments began on Wednesday at the state courthouse in Austin.
The court is expected to issue a decision by the end of June.