In June 1982, with ten other dissidents, Kronn helped organize the Group to Establish Trust between the U.S. and the USSR, a non-official movement for trust and peace between the Soviet Union and the West. The Trust Group avoided criticizing their own government’s policies, both because they believed that criticism would generate opposition, and because it was illegal to do so. Instead, they suggested ways to improve relations between the superpowers based on the belief that improved trust could slow or stop the arms race. Their proposals included ideas for conversion of the military-industrial complexes on both sides by shifting to joint work on peaceful, humanitarian projects.

As a result of these and other actions, Soviet authorities applied pressure on Kronn. New York Times Moscow correspondent John F. Burns reported that Kronn had been warned at the institute where he was employed that he faced dismissal and possible prosecution for treason if his dissident activities continued. In the summer of 1982, while an international peace march was taking place in Moscow, assault charges were fabricated against Kronn and an associate; Yuri Medvedkov, and the two were arrested on July 16 and held in prison by the Soviet security department, also known as the KGB, until July 31, 1982. Despite attempts to silence him, Kronn persisted with his unsanctioned political activities. In 1987 he chaired the Disarmament Section of the first Moscow International Symposium for Humanitarian Problems.

• Organized, with ten other Russian dissidents, the ‘Trust Group’ which was the first independent peace movement in the history of Russia.
• In 1987 Dr. Kronn again made history, when he chaired the Disarmament Section of the first ‘Moscow International Symposium for Humanitarian Problems” which was broadcast around the world.