Hyams worked in television through the early to mid-1970s. His first major film was Capricorn One (1978), a critically acclaimed conspiracy thriller about a faked mission to Mars. This was followed by the less successful Hanover Street (1979) which starred Harrison Ford, a rewrite of Ted Leighton's screenplay for the Steve McQueen film The Hunter (1980), and the science fiction cult classic Outland (1981), which starred Sean Connery in a 'High Noon' scenario set on Io, one of Jupiter's moons. In 1983, he produced, directed, and wrote the screenplay for 2010 (1984), collaborating closely with author Arthur C. Clarke (2010).