(CNN) A new genre of employment discrimination cases that could be the next battleground for supporters of LGBT rights are hurtling towards the Supreme Court.

More than two years after the Supreme Court cleared the way for same-sex marriage nationwide, plaintiffs want the justices to enable employees to use existing civil rights law to sue for discrimination based on sexual orientation.

On Tuesday, a federal appeals court based in New York will hear arguments in one such case, and later this fall the Supreme Court will consider whether to take up a separate challenge.

At the heart of the cases are whether Title VII of the Civil Rights Act of 1964, a federal law that bans employment discrimination because of sex, also protects claims of sexual orientation. In an unusual twist in the case, the Trump administration is on opposite sides from the Equal Employment Opportunity Commission -- a federal agency charged with enforcing Title VII.

Joshua Matz, a lawyer who has has written about the issue for the Take Care law blog, said the Supreme Court will likely take up the issue. "It's a matter of national importance, affecting employees and employers from every walk of life," he said.

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