[3] The museum is the resting place of Ham, the chimpanzee who, in 1961, became the first great ape to fly into space.

The Museum Support Center is an offsite warehouse and workshop that prepares items for display.

[2]: 57–58 [4] The John P. Stapp Air and Space Park is an outdoor exhibit area holding large artifacts, including the Sonic Wind No.

Ham, the chimpanzee who in 1961 became the first ape in space, is buried at the museum in front of the flagpoles.

In 1973 former Alamogordo mayor Dwight Ohlinger was inspired by the National Baseball Hall of Fame and Museum in Cooperstown, New York, to propose a Space Hall of Fame, and further to propose that it be built at Alamogordo because so much of the developmental work for the space program had been done in the Tularosa Basin.

[2]: 35  Ohlinger rallied support among elected officials at the local, state, and national levels, and Governor Bruce King adopted the idea into the Office of Cultural Affairs.

[2]: 40, 44  At the dedication ceremony the initial fifteen Hall of Fame members were inducted.

[2]: 51  The combined facility was named after Clyde Tombaugh, New Mexico resident and discoverer of Pluto.

In 1987 the name of the facility was changed to Space Center, reflecting the growing role of the exhibits.