From 1985 to 1989, Crespo served as Chief of Staff of the Argentine Air Force under President Raúl Alfonsín.

During the Carapintadas conflict within the Argentine Army, Crespo's leadership was instrumental in maintaining the Air Force's support for the democratic government.

[4] During his tenure, the Condor Program, a missile development initiative, was publicly revealed.

The program was later discontinued in the early 1990s under President Carlos Menem due to political pressure from the United States.

His death marked the end of a distinguished career in the Argentine military, remembered for his strategic acumen and commitment to national defense.