From October 1970 to July 1971, Nagel was an F-100 pilot with the 68th Tactical Fighter Squadron at England Air Force Base, Louisiana. He served a 1-year tour of duty as a T-28 instructor for the Laotian Air Force at Udorn RTAFB, Udorn, Thailand, prior to returning to the United States in October 1972 to assume A-7D instructor pilot and flight examiner duties at England Air Force Base, Louisiana. Nagel attended the USAF Test Pilot School at Edwards Air Force Base, California, from February to December 1975; and in January 1976, he was assigned to the 6,512th Test Squadron located at Edwards. As a test pilot, he has worked on various projects which have included flying the F-4 and A-7D.

He has logged 8,000 hours flying time--5,250 hours in jet aircraft.

Nagel first flew as a mission specialist on the crew of STS-51G which launched from the Kennedy Space Center, Florida, on June 17, 1985. The crew on board the Orbiter Discovery deployed communications satellites for Mexico (Morelos), the Arab League (Arabsat), and the United States (AT&T Telstar). They used the Remote Manipulator System (RMS) to deploy and later retrieve the SPARTAN satellite which performed 17 hours of x-ray astronomy experiments while separated from the Space Shuttle. In addition, the crew activated the Automated Directional Solidification Furnace (ADSF), six "Getaway Specials," participated in biomedical experiments, and conducted a laser tracking experiment as part of the Strategic Defense Initiative. After completing approximately 170 hours of space flight, Discovery landed at Edwards Air Force Base, California, on June 24, 1985.

Nagel then flew as pilot on the crew of STS-61A, the West German D-1 Spacelab mission, which launched from Kennedy Space Center, Florida, on October 30, 1985. This mission was the first in which payload activities were controlled from outside the United States. More than 75 scientific experiments were completed in the areas of physiological sciences, materials processing, biology, and navigation. After completing 111 orbits of the Earth, the Orbiter Challenger landed at Edwards Air Force Base, California, on November 6, 1985.

On his third flight, Nagel was commander of the STS-37 crew on board the Shuttle Atlantis, which launched into orbit on April 5, 1991, from Kennedy Space Center, Florida, and landed on April 11, 1991, at Edwards Air Force Base, California. During this mission the crew deployed the Gamma Ray Observatory (GRO) for the purpose of exploring gamma ray sources throughout the universe, and conducted the first scheduled space walk in more than five and one-half years. Also, the crew performed the first successful unscheduled space walk to free a stuck antenna on GRO.

Nagel also served as commander of STS-55, the German D-2 Spacelab mission. After launching on April 26, 1993, on the Shuttle Columbia, the crew landed 10-days later on May 6, 1993, at Edwards Air Force Base, California. During the ambitious mission 89 experiments were performed in many disciplines such as materials processing, life sciences, robotics, technology, astronomy and earth mapping.

With the completion of his fourth flight Nagel has logged a total of 723 hours in space.

Nagel retired from the Air Force, effective February 28, 1995. He retired from the Astronaut Office, effective March 1, 1995, to assume the full-time position of Deputy Director for Operations Development, Safety, Reliability, and Quality Assurance Office, Johnson Space Center, Houston, Texas. In September 1996, Nagel transferred to Aircraft Operations Division where he performs duties as a Research Pilot.