A lower court this summer overturned the ban on same-sex marriage that resulted from a statewide referendum on the issue, known as Proposition 8.
The lower court judge ruled that the ban violated the civil rights of gay Californians.
Due to enormous interest in the case, Monday's hearing in San Francisco is being nationally televised.
A three-judge panel will consider two aspects of the case.
Firstly, it will hear arguments about whether the group that successfully lobbied for the referendum is eligible to appeal against the lower court decision.
The judges will then consider the constitutionality of the ban itself.
Prop 8: California Gay Marriage Ban Overturned
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