A new collection of contemporary literature; Fixx on fame; The Random Review, edited by Gary Fisketjon and Jonathan Galassi. New York: Random House. 310 pp. $14.50 in hard cover, $3.95 in paperback.

Here is the first installment of a new annual offering, ''a critical survey of the best literary efforts - in short fiction, poetry, and the essay - from the full range of American periodicals.'' Actually, it seems an offspring of the old New American Review and the current Pushcart Prize anthologies.

Some of the poetry strikes me as contemporary antiestablishment-sentimental, and Frank Bidart's turbulent, turgid ''The War of Vaslav Nijinsky'' simply doesn't deserve the space it occupies; but there are lovely poems by Richard Blessing, ''At the Ballard Locks,'' and Linda Gregg, ''Death Looks Down.''

The pick of the nonfiction prose is Emile Capouya's complex, surprising autobiographical essay, ''In the Sparrow Hills.'' There is too much fiction that imitates the tactics of those contemporary archetypes, Ann Beattie and Raymond Carver, but the contributions from the originals themselves - Beattie's elegiac ''Jacklighting'' and Carver's savage ''Cathedral'' - are very impressive, indeed. I also admired Jean Thompson's vivid, troubling story, ''Remembering Sonny''; Patricia Zelver's conventional but well-constructed ''Unglued''; and Peter Taylor's ''The Gift of the Prodigal.''

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