NASA selected Hauck as an astronaut candidate in January 1978. He was assistant Crimson team Capcom for the first Space Shuttle mission re-entry. His first spaceflight was as pilot for STS-7, the seventh flight of the Space Shuttle, which launched from Kennedy Space Center, Florida, on June 18, 1983. The crew included Robert Crippen (spacecraft commander), and three mission specialists, John Fabian, Sally Ride, and Norm Thagard. This was the second flight for the orbiter Challenger and the first mission with a 5-person crew. During the mission, the STS-7 crew deployed satellites for Canada (ANIK-C2) and Indonesia (Palapa B-1); operated the Canadian-built Remote Manipulator System (RMS) to perform the first deployment and retrieval exercise (with the Shuttle Pallet Satellite (SPAS-01)); and with Crippen conducted the first piloting of the orbiter in close proximity to a free-flying satellite (SPAS-01). Mission duration was 147 hours before landing on a lakebed runway at Edwards Air Force Base, California, on June 24, 1983.

Hauck was spacecraft commander for the second mission of Discovery on mission STS-51-A, which launched on November 8, 1984. His crew included David M. Walker (astronaut) (pilot), and three mission specialists, Joseph Allen, Anna Fisher, and Dale Gardner. During the mission, the crew deployed two satellites, Telesat Canada's Anik D-2, and Hughes' LEASAT-1 (Syncom IV-1). In the first space salvage mission in history, the crew also retrieved for return to Earth the Palapa B-2 and Westar VI satellites. STS-51-A completed 127 orbits of the Earth before landing at Kennedy Space Center, Florida, on November 16, 1984.[3]