Moats was assigned in September 1955 to the Office of the Secretary of the Air Force, Washington, D.C., where he was chief of the Civil Branch, Community Relations Division.

In December 1957 he assumed command of the 60th Fighter Interceptor Squadron at Otis Air Force Base, Mass.

In July 1965 he became vice commander of the 401st Tactical Fighter Wing at England Air Force Base, La.

Moats returned to Europe in September 1970 as chief of the Joint U.S. Military Group-Military Assistance Advisory Group, Spain, and in October 1972 assumed command of Sixteenth Air Force.

On August 20, 1973, he was promoted to lieutenant general and appointed commander of the Sixth Allied Tactical Air Force with headquarters at Izmir, Turkey.