By John Updike, Bech at Bay. (Knopf, 241 pp.)

Bye-bye" is the last phrase in this final novel of Updike's Bech trilogy. Bech, like Harry in Rabbit at Rest, is wound down and winding up. "Enough," says Harry. "Bye-bye," says Bech. "Ditto," Updike himself seems to echo. The end of a lot of things is limned in these last books.

Like the other Bechs, this is a very funny book. It is also brilliantly sardonic, cryptic, acerbic, pathetic, nostalgic and poignant. In fact, the fun-poking humor behind all these sentiments derives unmistakably from Updike's unrelenting Bechian parody of the celebrity American writer, which he himself, of course, embodies. In the Jewish Henry Bech, the WASP Updike has attempted to create an eccentric but basically lovable alter ego.

Through Bech Updike enjoys saying things which he cannot say elsewhere. The classic case here is the surprising and outrageously funny chapter, "Bech Noir." With the help of his computer-whiz second wife, Robin ("Twenty-six, post-Jewish, frizzy, big hair"), Bech diabolically dispatches--murders--no fewer than four of his despised longtime critics. Updike is careful to blend characteristics so that no libel suits will be filed, but his descriptions of what these Bech critics have said show unmistakable traces of the caustic criticisms well-known pundits have leveled against Updike over the years.

One also feels the author standing in the shadows in the last chapter, "Bech and the Bounty of Sweden," in which Bech by default is awarded the Noble Prize in literature. Most of Updike's admirers know that he has been nominated for that prize many times without success. Bech reflects the determined sentiment of a man who thinks it unlikely this award will ever come: "Now an old man, he saw through dimmed eyes. He had done what he could; he had tried to write his own books rather than books others wanted him to write."

Other Updike themes emerge, including his love of America, its basic freedoms and its immigrant history--a patriotism Gore Vidal once unconscionably derided as a loyalty "to every far-out far-right piety currently being fed us." "America has its rough spots," says a sombered "Bech in Czech." "If the muggers don't get your wallet, the nursing homes will--but it's still a country that never had a pogrom."

Updike's preoccupations with finitude and personal transience, with all their attendant religious overtones, also appear here. "Bech's seven books glimmered in his backward glance like fading trailmarks in a dark wood, una selva oscura, the tangled place where his consciousness intersected with the universe." Updike explored the same theme rather grandly in his recent novel Toward the End of Time.

Typically, Bech's writer's block appears when he tries composing his Nobel acceptance speech. Nothing Updike has written will quite touch the heart as do the book's final pages when Bech attempts to deliver the speech. A painfully anguished effort at humor culminates in an emotionally surprising scene. Updike could not have chosen a better epigraph for the book than Wallace Steven's "Something of the unreal is necessary to fecundate the real." In Updike's capable hands, the fictional Bech becomes touchingly real indeed.