| | 1937 | LOST HORIZON | Best Music (Score) Nomination |
| | 1939 | MR. SMITH GOES TO WASHINGTON | Best Music (Scoring) Nomination |
| | 1941 | THE CORSICAN BROTHERS | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| | 1943 | THE MOON AND SIXPENCE | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| | 1944 | THE BRIDGE OF SAN LUIS REY | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| | 1949 | CHAMPION | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
 | 1952 | HIGH NOON | Best Music (Scoring of a Dramatic or Comedy Picture) Oscar |
 | 1952 | HIGH NOON | Best Music (Song) Nomination (shared with Ned Washington) For the song "High Noon (Do Not Forsake Me, Oh My Darlin')" |
 | 1954 | THE HIGH AND THE MIGHTY | Best Music (Scoring of a Dramatic or Comedy Picture) Oscar |
| | 1954 | THE HIGH AND THE MIGHTY | Best Music (Song) Nomination (shared with Ned Washington) For the song "The High and the Mighty" |
| | 1956 | FRIENDLY PERSUASION | Best Music (Song) Nomination (shared with Paul Francis Webster) For the song "Friendly Persuasion (Thee I Love)" |
| | 1956 | GIANT | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| | 1957 | WILD IS THE WIND | Best Music (Song) Nomination (shared with Ned Washington) For the song "Wild is the Wind" |
 | 1958 | THE OLD MAN AND THE SEA | Best Music (Scoring of a Dramatic or Comedy Picture) Oscar |
| | 1959 | THE YOUNG LAND | Best Music (Song) Nomination (shared with Ned Washington) For the song "Strange are the Ways of Love" |
| | 1960 | THE ALAMO | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| | 1960 | THE ALAMO | Best Music (Song) Nomination (shared with Paul Francis Webster) For the song "The Green Leaves of Summer" |
| | 1961 | TOWN WITHOUT PITY | Best Music (Song) Nomination (shared with Ned Washington) For the song "Town Without Pity" |
| | 1961 | THE GUNS OF NAVARRONE | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| | 1963 | 55 DAYS AT PEKING | Best Music (Song) Nomination (shared with Paul Francis Webster) For the song "So Little Time" |
| | 1963 | 55 DAYS AT PEKING | Best Music (Score - Substantially Original) Nomination |
| | 1964 | THE FALL OF THE ROMAN EMPIRE | Best Music (Score - Substantially Original) Nomination |
| | 1971 | CHAIKOVSKY (1969)* | Best Music (Scoring Adaptation and Original Song Score) Nomination |