Remek was an active member both in the Pioneers and the Czechoslovak Union of Youth. He studied mathematics and physics at middle school in Čáslav where he earned awards in track running the 400-meter, 800-meter, and 1,500-meter events. Remek graduated in 1966 and proceeded to "Vyšší Letecké Učiliště", an aviation school in Košice, where he trained in an Aero L-29 Delfín. Remek graduated in 1970 and was commissioned as a lieutenant in the Czechoslovak Air Force. Remek served as a fighter pilot, flying MiG-21s in the 1st Fighter Air Regiment. In the 1970s Remek married his first wife, Czech actress Hana Davidová, the daughter of politician Václav David. They had a daughter together, Anna, in 1980. He had a second daughter, Jana, three years after the first, with his second wife, also called Jana.