"Rocky," a romantic fable about the rehabilitation of an obscure prize-fighter, and "Network," a vitriolic satire about the television industry, emerged as co-favorites in the 1976 Academy Awards race following the announcement of nominations yesterday in Los Angeles. Each picture received 10 Oscar nominations, including best movie of the year.

"All the President's Men," the movie version of the Bob Woodward Carl Bernstein casebook on the Watergate story, took the runner-up spot with eight nominations and will challenge for the top award, along with "Taxi Driver" and "Bound for Glory." The winners will be revealed at the 49th annual Oscar ceremony on Monday, Mar. 28.

The late Peter Finch, cited for his performance as a demented newscaster in "Network," became the third actor in Academy annuals to receive a nomination posthumously. The others were James Dean for "Giant" in 1956 and Spencer Tracy for "Guess Who's Coming to Dinner?" in 1967.The eventual award-winners in those years were Yul Brynner and Rod Steiger, respectively. Finch died of a heart attack last month.

Finch's co-star in "Network," William Holden, was also nominated for best actor. Holden won the award in 1953 for his performance in "Stalag 17." Sylvester Stallone, the young star of "Rocky," which he also wrote, became only the third person in Academy history to be nominated for performing and screenwriting awards in the same year. The others were Charles Chaplin for "The Great Dictator" in 1940 and Orson Welles for "Citizen Kane" in 1941. The final two nominees for best actor were Robert De Niro in "Taxi Driver" and Italian star Giancarlo Giannini in "Seven Beauties."

The female star of "Network," Faye Dunaway, will contend for the best actress award with Sissy Spacek of "Carrier," Talia Shire of "Rocky" and two Europeans, Liv Ullmann of "Face to Face" and Marie-Christine Barrault of "Cousin, Cousine." Dunaway has been nominated twice before - for "Bonnie & Clyde" and "Chinatown" - but has never won. Ullmann was a best actress nominee in 1972 for "The Emigrants," while Shire, the sister of director Francis Ford Coppola, received a supporting actress nomination in 1974 for "The Godfather, Part II."

The 1976 nominees for supporting actress are Jane Alexander in "All the President's Men," Jodie Foster in "Taxi Driver," Lee Grant (last year's winner in this category for "Shampoo") in "Voyage of the Damned," Piper Laurie in "Carrie" and Beatrice Straight in "Network." and Alan J. Pakula for "All the President's men." The remaining spots in the directing category went to Ingmar Bergman for "Face to Face," his last Swedish production, and Lina Wertmuller for "Seven Beauties." Both Bergman for Wertmuller are currently shooting English language productions.

Stallone appears to face formidable competition for best original screenplay from Paddy Chayefsky, the author of "Network." The other nominees are Wertmuller for "Seven Beauties," Walter Bernstein for "The Front" and French filmmakers Jean-Charles Tacchella and Daniele Thompson for "Cousin, Cousine." The finalists for best adaptation are William Goldman with "All the President's Men," Robert Getchell with "Bound for Glory," Nicholas Meyer with "The Seven-Per Cent Solution," Fredrico Fellini and Berbardino Zapponi with "Fellini's Casanova" and Steve Shagan and David Butler with "Voyage of the Damned."

Although Barbra Streisand failed to win an acting nomination for her starring role in "A Star is Born," she was nominated for a song-writing award.

"Evergreen," a love ballad from the film, with lyrics by Paul Williams and music by Streisand, was one of the five nominees for best song. The others were "Ave Satani" from "The Omen," music and lyrics by Jerry Goldsmith; "Come to Me" from "The Pink Panther Strikes Again," music by Henri Mancini and lyrics by Don Black; "Gonna Fly Now" from "Rocky," music by Bill Conti and lyrics by Caroll Conners and Ayn Robbins; and the mystery entry, "A World That Never Was," from something called "Half a House," music by Sammy Fain and lyrics by Paul Francis Webster.

The late composer Bernard Hermann received two nominations for best original score: "Obsession" and "Taxi Driver." The remainning nominees were Goldsmith for "The Omen," Jerry Feilding for "The Outlaw Josey Wales" and Lalo Schifrin for "Voyage of the Damned."

Nominations in other categories:

Best Original Song Score or Musical Adaptation:

"Bound for Glory," Leonard Rosenman; "Bugsy Malone," Paul Williams; "A Star is Born," adaptation by Roger Kellaway.

Cinematography: "Bound to Glory," Haskell Wexler; "King Kong," Richard H. Kline; "Logan's Run," Ernest Laszlo; "Network," Owen Roizman; "A Star is Born," Robert Surtees.

Editing: "All the President's Men," Robert L. Wolfe; "Bound for Glory," Robert Jones and Pembroke J. Herring; "Network," Alan Heim; "Rocky," Richard Halsey and Scott Conrade; "Two-Minute Warning," Eve newman and Walter Hannemann.

Art Direction: "All the President's Men," George jenkins, with set decorations by George Gaines; "The Incredible Sarah," Elliott Scott and Norman Reynolds; "The Last Tycoon," Gene Callahan, Jack COllis and Jerry Wunderlich; "Logan's Run," Dale Hennesy and Robert de Vestel; "The Shootist," Robert Boyle and Arthur Parker.

Costume Design: "Bound for Glory," William These; "Fellini's Casanova," Danilo Donati; "The Incredible Sarah," Anthony Mendieson; "The Passover Plot," Mary Wills; and "The Seven-Per-Cent Solution," Alan Barrett.

Foreign Language Film: "Black and White in Color," Ivory Coast; "Cousin, Cousine," France; "Jacob and Liar," East Germany; "Nights and Days," Poland; "Seven Beauties," Italy.

Sound: "All the President's Men," Arthur Piantadosi, Les Fresholtz, Dick Alexander and Jim Webb; "King Kong," Harry Warren Tetrick, William McCaughey, Aaron Rochin and Jack Solomon; "Rocky," Tetrick, McCaughey, Lyle Burbridge and Michael Kohut; "The Silver Streak," Donald Mitchell, Douglas Williams, Richard Tyler and Hal Etherington; "A Star is Born," Robert Knudson, Dan Wallin, Robert Glass and Tom Overton.

Documentary Feature: "Harlan County, U.S.A.," "Hollywood on Trial," "Off the Edge," "People of the Wind" and "Volcano: An inquiry into the Life and Death of Malcolm Lowry."

Documentary Short Subject: "American Shoeshine," "Blackwood," "The End of the Road," "Number Our Days" and "Universe."

Animated Short Subject: "Dealo," "Leisure" and "The Street."

Live-Action Short Subject: "In the Region of Ice," "Kudzu," "The Morning Spider," "Nightlife" and "Number One."