The case is an appeal by the F.C.C. of a ruling in 2010 by the United States Court of Appeals for the Second Circuit that said the commission’s policy against “fleeting expletives” and other indecency, which it measures on a case-by-case basis, was “unconstitutionally vague.”

The Supreme Court reframed the case slightly, saying it would hear arguments only on whether the F.C.C.’s “indecency enforcement regime” violated the free speech or due process clauses of the Constitution.

At issue are two live broadcasts on the Fox network of the Billboard Music Awards. In the first, in 2002, Cher used an obscenity while accepting an award. In 2003, Nicole Richie, while presenting an award, used two vulgarities in explaining how hard it was to remove cow manure from a purse.

The Supreme Court will also consider whether the appeals court was warranted in overturning a fine against ABC stations for the 2003 broadcast of an episode of the then-popular ABC series “NYPD Blue” that included a naked woman.

The Fox case has previously come before the court. In 2009, the Supreme Court ruled in a 5-4 decision that the commission had followed proper administrative procedures when it invoked the ban on expletives during certain hours against broadcasters. But several justices, including at least one on each side of the decision, expressed skepticism that the ban on expletives was constitutional.