| Mulan | 1998 | Best Music, Original Musical or Comedy Score | Nominee |
| L.A. Confidential | 1997 | Best Music, Original Dramatic Score | Nominee |
| Basic Instinct | 1992 | Best Music, Original Score | Nominee |
| Hoosiers | 1986 | Best Music, Original Score | Nominee |
| Under Fire | 1983 | Best Music, Original Score | Nominee |
| Poltergeist | 1982 | Best Music, Original Score | Nominee |
| Star Trek: The Motion Picture | 1979 | Best Music, Original Score | Nominee |
| The Boys From Brazil | 1978 | Best Music, Original Score | Nominee |
| The Omen | 1976 | Best Music, Original Score Best Music, Song (for the song "Ave Satani") |
WINNER Nominee |
| The Wind and The Lion | 1975 | Best Music, Original Score | Nominee |
| Chinatown | 1974 | Best Music, Original Dramatic Score | Nominee |
| Papillon | 1973 | Best Music, Original Dramatic Score | Nominee |
| Patton | 1970 | Best Music, Original Score | Nominee |
| Planet of The Apes | 1968 | Best Music, Original Score for a Motion Picture (not a Musical) | Nominee |
| The Sand Pebbles | 1966 | Best Music, Original Music Score | Nominee |
| A Patch of Blue | 1965 | Best Music, Score - Substantially Original | Nominee |
| Freud | 1962 | Best Music, Score - Substantially Original | Nominee |
| L. A. Confidential | 1997 | Best Original Score - Motion Picture | Nominee |
| Basic Instinct | 1992 | Best Original Score - Motion Picture | Nominee |
| Under Fire | 1983 | Best Original Score - Motion Picture | Nominee |
| Star Trek: The Motion Picture | 1979 | Best Original Score - Motion Picture | Nominee |
| Alien | 1979 | Best Original Score - Motion Picture | Nominee |
| Chinatown | 1974 | Best Original Score - Motion Picture | Nominee |
| Star Trek: Voyager | 1995 | Outstanding Individual Achievement in Main Title Theme Music | WINNER |
| Masada | 1981 | Outstanding Music Composition for a Series (Dramatic Underscore) | WINNER |
| Babe | 1975 | Outstanding Achievement in Music Composition for a Special | WINNER |
| QB VII | 1974 | Unverified | WINNER |
| The Man from U.N.C.L.E. | 1964 | Unverified | Nominee |
| Thriller | 1960 | Unverified | Nominee |
| Warklock | 1988 | Unverified | Nominee |
| Link | 1986 | Unverified | Nominee |
| Gremlins | 1984 | Unverified | WINNER |
| Star Trek: The Motion Picture | 1979 | Unverified | Nominee |
| L.A. Confidential | 1997 | BAFTA Film Award | Nominee |
| Alien | 1979 | Anthony Asquith Award for Film Music | Nominee |
| The Wind and the Lion | 1975 | Anthony Asquith Award for Film Music | Nominee |
| Chinatown | 1974 | Anthony Asquith Award for Film Music | Nominee |
| Annie Awards | Mulan - 1998 | Outstanding Individual Achievement for Music in an Animated Feature Production | WINNER |
| Palm Springs International Film Festival | n/a - 1998 | Lifetime Achievement Award for Film Music | WINNER |
| Golden Satellite Awards | L.A. Confidential - 1997 | Best Motion Picture Score | Nominee |
| Richard Kirk Award | Unverified - 1985 or 1986? | BMI Lifetime Achievement Award? | WINNER |