"The Making of the Atomic Bomb," historian Richard Rhodes' account of the birth of the first nuclear weapons, won its second major literary award yesterday when the National Book Critics Circle announced the winners of its annual awards for the best books of 1987.

The nonfiction prize for the Rhodes book (Simon and Schuster), winner of the National Book Award two months ago, puts it within striking distance of the literary world's triple crown, which also includes the Pulitzer Prize, announced in April.

Philip Roth's novel "The Counterlife" won the Critics Circle fiction prize, and C. K. Williams' "Flesh and Blood" the poetry award. Two posthumously published books -- Donald R. Howard's "Chaucer: His Life, His Works, His World" and Edwin Denby's "Dance Writings" -- received the NBCC prizes for biography and criticism, respectively.

At its meeting in New York yesterday, the NBCC board of directors also voted to present its seldom-given citation for "distinguished contributions to the enhancement of American literary and critical standards" to Robert Giroux, the 73-year-old editor-in-chief and partner in the publishing house Farrar, Straus & Giroux.

In his nearly 50 years in publishing, Giroux has edited T. S. Eliot, E. M. Forster, George Orwell, Edmund Wilson, Jean Stafford, Robert Lowell, Flannery O'Connor, Randall Jarrell, Hannah Arendt, Susan Sontag, Peter Taylor and Saul Bellow, to name only a famous few.

The NBCC board of directors also presented its annual citation for the best book reviewing of the past year to Brooklyn-based free-lancer Josh Rubins, whose cited reviews appeared in The New York Review of Books and The Nation. The formal ceremonies honoring the winners and their publishers will take place at New York University Jan. 28.

According to board members present during yesterday's six hours of deliberations at the Algonquin Hotel, the most heated discussion and closest voting centered around the nonfiction award. The Rhodes book's closest competitor, they said, was journalist Randy Shilts' bestselling book on the AIDS crisis, "And the Band Played On."

One critic is said to have praised the Shilts book for "altering the way I perceive the news," but others faulted it for its occasional "melodrama" and "stridency." Another critic participating in the discussion said, "It needed to be edited but it wasn't." The Rhodes book, by contrast, was considered to be "definitive history," and ultimately dominated the informal voting that leads to consensus among the board.

Roth's "The Counterlife" (Farrar, Straus & Giroux) had been expected to face its stiffest competition from Toni Morrison's "Beloved" for the fiction prize, but the latter novel quickly faded as unanticipated board sentiment emerged for Tom Wolfe's "The Bonfire of the Vanities." After discussion including the remark that Wolfe had written a "cartoon novel" whose women characters were "all bimbos," the board voted in favor of Roth's apparently final Nathan Zuckerman novel.

Another premeeting favorite, Robert Lowell's "Collected Prose" in the criticism category, could not survive an apparent board groundswell for the dance criticism of Denby, who committed suicide three years ago. Denby's book, published by Knopf, was compared by one new convert on the board to James Agee's film criticism in its range and originality, while Lowell's critical pieces were felt to suffer, in one view, from "a deeply uncritical element."

In the biography and autobiography category, Howard's book on Chaucer (Dutton) prevailed over its chief competitor, S. J. Perelman's collected letters -- which were compared by one board member to being "invited to a four-hour cocktail party and being required to drink only vinegar on the rocks." Howard, a professor of English at Stanford, died last year of AIDS.

"Flesh and Blood" (Farrar, Straus & Giroux), the latest volume of poetry by C. K. Williams, won broad approval from the critics, who noted especially the last poem in the book, "Le Petit Salvie'."

Children's Book Awards The nation's principal honors for children's literature, the Newbery and Caldecott awards, were announced yesterday as well, at the midwinter meeting of the American Library Association in San Antonio.

The John Newbery Medal for children's literature was bestowed on Russell Freedman's "Lincoln: A Photo Biography" (Clarion Books), with honorable mentions to Norma Fox Mazer's "After the Rain" (Morrow) and Gary Paulsen's "Hatchet" (Bradbury).

The Randolph Caldecott Medal, for the best children's book illustration of 1987, was given to John Schoenherr for his work on "Owl Moon" by Jane Yolen (Philomel). John Steptoe, who illustrated a traditional African folk tale he calls "Mufaro's Beautiful Daughters" (Lothrop, Lee & Shepard), received honorable mention. The book also won the Coretta Scott King award, for excellence in children's literature about the black experience, at the San Antonio meeting yesterday.