| Year | Category | Movie | Win/Nominated |
|---|---|---|---|
| 1990 | Best Score | Ghost (1990) | Nominated |
| 1988 | Best Score | Gorillas in the Mist (1988) | Nominated |
| 1985 | Best Score | Witness (1985) | Nominated |
| 1984 | Best Original Score | Passage to India (1984) | Win |
| 1972 | Best Song | Life and Times of Judge Roy Bean (1972) | Nominated |
| 1965 | Best Original Score | Doctor Zhivago (1965) | Win |
| 1962 | Best Original Score | Lawrence of Arabia (1962) | Win |
| Year | Category | Movie | Win/Nominated |
|---|---|---|---|
| 1989 | Best Original Film Score | Dead Poets Society (1989) | Win |
| 1985 | Best Score | Passage to India (1984) | Nominated |
| 1985 | Best Score | Witness (1985) | Win |
| Year | Category | Movie | Win/Nominated |
|---|---|---|---|
| 1999 | Best Original Score | Sunshine (2000) | Nominated |
| Year | Category | Movie | Win/Nominated |
|---|---|---|---|
| 2000 | Best Original Score | Sunshine (2000) | Nominated |
| 1995 | Best Original Score | Walk in the Clouds (1995) | Win |
| 1988 | Best Original Score | Gorillas in the Mist (1988) | Win |
| 1984 | Best Original Score | Passage to India (1984) | Win |
| 1975 | Best Original Score | Man Who Would Be King (1975) | Nominated |
| 1972 | Best Original Song | Life and Times of Judge Roy Bean (1972) | Nominated |
| 1966 | Best Original Score | Is Paris Burning? (1966) | Nominated |
| 1965 | Best Original Score | Doctor Zhivago (1965) | Win |
| 1962 | Best Original Score | Lawrence of Arabia (1962) | Nominated |