Shunya (later renamed Alexander) Gelman was born in Donduşeni (now in Moldova), a Bessarabian village that had been part of the Russian Empire before it was returned to Romania during the Russian Civil War and Soviet annexation in 1940. His parents were Isaak Davydovich Gelman (1904—1981) and Manya Shayevna Gelman (1910—1942). After the Nazi attack on the Soviet Union in 1941, the occupying German forces deported the Gelman family to the Bershad ghetto in Transnistria, where his mother died. Only Alexander Gelman and his father (from 14 deported members) survived a death march upon leaving the camp near the end of the war.