From 1934 to 1936 Hessen was a deputy director of the Physics Institute in Moscow headed by S.I. Vavilov. On 22 August 1936 Hessen was arrested by the NKVD on charges of participation in a counter-revolutionary terrorist organization and preparation of terrorist acts. He was secretly tried for terrorism by a military tribunal together with his gymnasium school teacher Arkadij O. Apirin, who had been arrested two months earlier.