LOS ANGELES, April 25— Kent Smith, an actor whose stage, film and television work spanned four decades and included roles in the movies ''Cat People'' in 1942 and ''Pete 'n' Tillie'' in 1972, died of heart disease Tuesday at the Motion Picture and Television Hospital. He was 78 years old.
Mr. Smith, who was born in New York in 1907, acted on Broadway in ''Measure for Measure,'' ''Sweet Love Remembered,'' ''The Best Man'' and ''Ah, Wilderness.''
But he was best known for his work in the 1940's films ''Cat People,'' ''The Fountainhead'' and ''The Spiral Staircase.'' He also appeared in the movies ''Hitler's Children'' in 1942, ''This Land Is Mine'' in 1943, ''Nora Prentiss'' and ''Magic Town'' in 1947, and ''The Voice of the Turtle'' in 1948.
Later films included ''The Damned Don't Cry,'' ''Comanche'' ''Death of a Gunfighter'' and ''Pete 'n' Tillie.''
Mr. Smith also appeared on numerous television shows, including ''Peyton Place,'' where he played Dr. Robert Morton, ''Outer Limits,'' ''The Invaders'' and ''Profiles in Courage.''
Mr. Smith is survived by his wife, Edith, and a daughter.
