"The Collected Stories of John Cheever" received the fiction award and Garry Wills' "Inventing America" the general nonfiction award of the National Book Critics Circle last night in New York.

The three other books honored by the organization of some 200 literary critics and editors were: "Hello Darkness: The Collected Poems of L.E. Sissman" (Poetry); Meyer Schapiro's "Modern Art: 19th and 20th Centuries" (Criticism); and Maureen Howard's autobiographical "Facts of Life" (also in General Nonfiction).

"The Collected Stories of John Cheever," a national bestseller, gathers together the work of three decades by one of the most acclaimed short story writers of our time. Among Cheever's celebrated stories of love and disillusionment in the suburbs of New York and Connecticut are "The Enormous Radio," "The Swimmer" and "The Country Husband" with its famous closing lines: "Then it is dark: it is a night where kings in golden suits ride elephants over the mountains."

"Inventing America" is Garry Wills" detailed and deft study of the historical and philosophical backgrounds to Jefferson's Declaration of Independence. By examining the language of the familiar document, phrase by phrase, and by relating its ideas to those of the science and spirit of the 18th century, Wills elucidates the principles behind the founding of our nation. "To understand a text from the past," he has said, "one must reassemble a world around that text."

"Hello, Darkness," the collected poems of the late L.E. Sissman, was a clear favorite of the NBCC Board of Directors. In the final years before his death in 1976 from Hodgkins' disease, Sissman wrote wittily about the vicissitudes of ordinary life and with quiet courage about his illness in poems like "Homage to Clotho,. A Hospital Suite."

Meyer Schapiro, a distinguished art historian at Columbia University, is a specialist in early Christian and Byzantine art, but he has also written the important papers on Cezanne, Picasso and abstract painting that meke up "Modern Art: 19th and 20th Centuries."

Novelist Maureen Howard's "Facts of Life," a memoir about growing up in Bridgeport, Conn., was the other winner of a new dual award for general nonfiction. Because of the wide range of books that fall into this category, the NBCC last year decided that two selections would more adequately cover biography and autobiography, history and science.

The closest voting of the evening occurred in the fiction category when Cheever's stories were chosen over the strong runner-up, "The World According to Garp" by John Irving. Certain of the 16 criyics of the board who made the final selections felt that the award to Cheever was also a way of acknowledging his lifetime contribution to American letters. Sissela Bok's philosophical study, "Lying" was also a close contender in the General Nonfiction category.

The National Book Critics Circle, established in 1974, began its award program in 1975. (E. L. Doc torow's "Ragtime" received the fiction prize that year.) Unlike the National Book Awards (with which it is sometimes confused), the NBCC awards carry no cash prize and reflect not the taste of small juries selected for each category, but the judgment of some 200 book critics and literary editors from around the country.