A judge could order New Jersey to allow gay marriages after a hearing is held.
A group of gay couples has asked the judge to both allow gay marriage and to recognize gay marriages performed in other states.
Arguments are set for Thursday morning in a state courthouse in Trenton.
New Jersey now allows only civil unions for same-sex couples.
The plaintiffs argue the state is discriminating against them since the U.S. Supreme Court in June invalidated key parts of a ban on giving federal benefits to married gay couples.
Lawyers for the state say couples united in civil unions can obtain some federal benefits even if New Jersey doesn’t recognize gay marriage.
They say it’s the federal government’s fault, not the state’s, if some of those couples are being denied certain federal benefits.