His first assignment for a spaceflight was in June 1965 as a liaison officer (Capcom) for the Gemini 4 mission, during which Edward White performed the first American spacewalk.
On March 21, 1966, he was nominated as the backup pilot for the Gemini 10 spaceflight, which took place in June of that year. Had Michael Collins been unable to participate, Williams would have been the third American to perform a spacewalk.
Williams served as liaison for the Gemini 11 flight in September 1966. Afterward, he was assigned to the Apollo program and trained as a lunar module pilot. On December 22, 1966, NASA announced the planned crews for the second and third Apollo flights, provisionally designated Mission D and Mission E. Williams, along with Pete Conrad and Richard Gordon, formed the backup crew for Mission E. All plans were put on hold following the Apollo 1 disaster on January 27, 1967.
Williams died in a plane crash on October 5, 1967, when the controls of his T-38 failed. He attempted an emergency ejection, but activated the ejection seat too late or in an unsuitable flight attitude, so his parachute did not open in time. He was buried in Arlington National Cemetery.
Alan Bean took Pete Conrad’s place in the crew. Conrad, Gordon, and Bean later became the backup crew for Apollo 9 and, in November 1969, carried out the second lunar landing with Apollo 12. Their mission badge featured four stars: three for the crew members and the fourth for Clifton Williams.