Box played trumpet in the United States Marine Band; produced music (composed, arranged, recorded, conducted) for major radio markets in the North America, London, Luxembourg, and Australia.
He composed film music for Braniff International Airways, Dr. Pepper, Buick, the United States Navy, Haggar Slacks, Zale Corporation, Texas Instruments, LTV Aerospace, and Bell Helicopter.
He recorded and conducted for various artists including Stevie Wonder, Boz Scaggs, Glen Campbell, Lou Rawls, Charlie Rich, and Chet Atkins.
In 1974, Euel, as composer, and his wife, Betty, as lyricist, received a Golden Globe Award for Best Original Song — "I Feel Love" — from the film Benji.
Benji earned Euel Box and his wife, Betty, a 1975 nomination for an Oscar and won a Golden Globe Award for Best Song From a Motion Picture.