A three-judge panel will hear arguments about gay marriage bans in the three states, setting up a possible decision that could allow gay marriages to go ahead.
The hearings before the US Court of Appeals for the 5th Circuit come as momentum builds nationwide to allow same-sex marriage, which is now legal in 36 states.
Also on Friday, US Supreme Court justices will meet in private to decide whether to add cases on the issue to their calendar this term.
The suit in Texas, which is the most populous state where gay marriage remains illegal, was filed on behalf of Austin residents Cleopatra De Leon and Nicole Dimetman, who were married in Massachusetts, and Victor Holmes and Mark Phariss, who were denied a marriage license when they applied in Texas.
In February, US District Judge Orlando Garcia ruled the Texas ban unconstitutional because it denied the couples equal protection under the law. Enforcement of the decision is on hold pending the appeal.
Proponents of the bans in Texas, Louisiana and Alabama have argued that states have the right to decide who can marry and that it is in the states' interests to promote marriage between a man and a woman.
In September, a US district judge upheld Louisiana's gay marriage ban, in what was a break from a string of recent rulings against such bans in other states that followed a US Supreme Court decision in June 2013 expanding federal recognition of same-sex marriages.
Two months later, a US district judge struck down as unconstitutional a same-sex marriage ban in Mississippi, overturning a measure that voters overwhelmingly approved about a decade ago.