In a display case in a room off the Inner Peristyle Garden at the J. Paul Getty Museum in Malibu, there is a small statue of a satyr, an ancient Greek half-man, half-beast figure that, when closely scrutinized, is obviously aroused.

Nearby, a vase from about 510 B.C.--attributed to Euthymides, a contemporary of the famed Greek vase maker Euphronios--is vividly illustrated with a scene depicting a couple engaged in what is clearly steamy foreplay.

And in the next room, another vase, discreetly titled "Drunken Singing Reveler and His Young Attendant," shows a pretty-faced teen-age boy holding a pitcher into which his older male companion is urinating.

Across town, at the Los Angeles County Museum of Art, a tall, phallic structure by Robert Graham includes numerous explicit scenes of sexual intercourse. Two or three rooms away, a couple makes love in the back seat of a 1938 Dodge.

In still another room, Jean-Simon Berthelemy's 1778 painting, "Death of a Gladiator," shows its subject complete with pubic hair. Philip Conisbee, the museum's curator of European painting and sculpture, points out that the work probably was completed by Berthelemy while he was in Rome, studying under a French government grant.

Except for the '38 Dodge scene--by Edward Kienholz, which caused a scandal over its content after it was completed in 1964--none of these anatomically explicit or sexually suggestive artworks has precipitated a single complaint by the millions of people who have viewed them in the last five years or so, the two museums say.

Even with the Kienholz, said Pamela Jenkinson, public information officer at the county museum, "we haven't heard squat since we opened the building."

Among curators at the Getty and at LACMA, this is a source of puzzlement. Why, when a single room at the Getty contains a dozen pieces of sexually explicit art, has similar subject matter in contemporary art caused such a fuss? Witness the ruckus surrounding the late photographer Robert Mapplethorpe, whose homoerotic and sadomasochistic work--except for its medium--focuses on many of the same things the ancient Greeks did.

Ironically, the single most controversial image in a disputed show of Mapplethorpe's work is a self-portrait in which he appears nude, with a bullwhip protruding from his buttocks in a fashion reminiscent of the bestial detail of Greek satyrs.