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| ASCAP Film and Television Music Awards | |||
| Year | Result | Award | Category/Recipient(s) |
|---|---|---|---|
| 1995 | Won | ASCAP Award | Top Box Office Films for: Wolf (1994) |
| 1994 | Won | ASCAP Award | Top Box Office Films for: In the Line of Fire (1993) |
| Lifetime Achievement Award | |||
| 1988 | Won | ASCAP Award | Top Box Office Films for: Untouchables, The (1987) |
| Academy Awards, USA | |||
| Year | Result | Award | Category/Recipient(s) |
| 2001 | Nominated | Oscar | Best Music, Original Score for: Malèna (2000) |
| 1992 | Nominated | Oscar | Best Music, Original Score for: Bugsy (1991) |
| 1988 | Nominated | Oscar | Best Music, Original Score for: Untouchables, The (1987) |
| 1987 | Nominated | Oscar | Best Music, Original Score for: Mission, The (1986) |
| 1979 | Nominated | Oscar | Best Music, Original Score for: Days of Heaven (1978) |
| BAFTA Awards | |||
| Year | Result | Award | Category/Recipient(s) |
| 1991 | Won | BAFTA Film Award | Best Original Film Score for: Nuovo cinema Paradiso (1988) Award shared with: Andrea Morricone |
| 1988 | Won | BAFTA Film Award | Best Score for: Untouchables, The (1987) |
| 1987 | Won | BAFTA Film Award | Best Score for: Mission, The (1986) |
| 1985 | Won | BAFTA Film Award | Best Score for: Once Upon a Time in America (1984) |
| 1980 | Won | Anthony Asquith Award for Film Music | for: Days of Heaven (1978) |
| César Awards, France | |||
| Year | Result | Award | Category/Recipient(s) |
| 1982 | Nominated | César | Best Music Written for a Film (Meilleure
musique) for: Professionnel, Le (1981) |
| 1980 | Nominated | César | Best Music Written for a Film (Meilleure
musique) for: I... comme Icare (1979) |
| David di Donatello Awards | |||
| Year | Result | Award | Category/Recipient(s) |
| 2001 | Nominated | David | Best Music (Migliore Musicista) for: Malèna (2000) |
| 2000 | Won | David | Best Music (Migliore Musicista) for: Canone inverso - making love (2000) |
| 1999 | Won | David | Best Music (Migliore Musica) for: Leggenda del pianista sull'oceano, La (1998) |
| 1993 | Won | David | Best Music (Migliore Musicista) for: Jona che visse nella balena (1993) |
| 1991 | Won | David | Best Music (Migliore Musicista) for: Stanno tutti bene (1990) |
| 1989 | Won | David | Best Music (Migliore Musicista) for: Nuovo cinema Paradiso (1988) |
| 1988 | Won | David | Best Music (Migliore Musicista) for: Occhiali d'oro, Gli (1987) |
| European Film Awards | |||
| Year | Result | Award | Category/Recipient(s) |
| 1999 | Won | Life Achievement Award | |
| Fantafestival | |||
| Year | Result | Award | Category/Recipient(s) |
| 1995 | Won | Career Award | |
| Golden Globes, USA | |||
| Year | Result | Award | Category/Recipient(s) |
| 2001 | Nominated | Golden Globe | Best Original Score - Motion Picture for: Malèna (2000) |
| 2000 | Won | Golden Globe | Best Original Score - Motion Picture for: Leggenda del pianista sull'oceano, La (1998) |
| 1992 | Nominated | Golden Globe | Best Original Score - Motion Picture for: Bugsy (1991) |
| 1990 | Nominated | Golden Globe | Best Original Score - Motion Picture for: Casualties of War (1989) |
| 1988 | Nominated | Golden Globe | Best Original Score - Motion Picture for: Untouchables, The (1987) |
| 1987 | Won | Golden Globe | Best Original Score - Motion Picture for: Mission, The (1986) |
| 1985 | Nominated | Golden Globe | Best Original Score - Motion Picture for: Once Upon a Time in America (1984) |
| Golden Satellite Awards | |||
| Year | Result | Award | Category/Recipient(s) |
| 2001 | Nominated | Golden Satellite Award | Best Original Score for: Malèna (2000) |
| 2000 | |||