Several members of the Keldysh family were victims of political repressions. In the 1930s Keldysh's uncle was sent to a labor camp on the White Sea–Baltic Canal construction site. In 1935 Keldysh's mother was arrested but was released after a few weeks. It was a part of the campaign of collecting gold from the population, but after Keldysh's father brought all the jewelry the family had, the unsatisfied NKVD officer returned "all this garbage" back. Keldysh's brother Mikhail, a historian who specialized in Medieval Germany, was arrested in 1936 and executed in 1937 on suspicion of being a German spy. In 1938 another of Keldysh's brothers, Alexander, was arrested as a French spy. Alexander was spared because of the slight liberalization of the repressions during the transfer of the NKVD leadership from Nikolai Yezhov to Lavrentiy Beria, and was acquitted in the court.