Arguments Tuesday morning focused on whether the sponsors of Prop. 8 are entitled to appeal last year's federal ruling that overturned the 2008 same-sex marriage ban.
The governor and attorney general have refused to appeal or defend the measure.
The court's ruling is due in three months. It will determine whether all initiative sponsors in California are legally entitled to defend their measures in state court.
The 9th U.S. Circuit Court of Appeals has expressed doubts about the ability of Proposition 8's sponsors to challenge the lower court ruling absent the involvement of California's governor or attorney general, both of whom agreed the ban was unconstitutional and refused to appeal.
But the 9th Circuit punted the question to the California Supreme Court earlier this year, saying it was a matter of state law. Although the appeals court still must decide for itself if Proposition 8's supporters are eligible under federal court rules to appeal the ruling that struck down the ban, the state court's input is likely to weigh heavily in its decision.
If the state Supreme Court says the ban's proponents did not have standing to appeal, and if the 9th Circuit and ultimately the U.S. Supreme Court ultimately agree, it could clear the way for same-sex marriages to resume in California.
If the court holds the proponents were qualified to appeal and the 9th Circuit agrees, the appeals court would then weigh the broader civil rights implications of Proposition 8. A decision on the ban's constitutionality is expected to be appealed to the U.S. Supreme Court.
The Associated Press contributed to this report.