 In the 1930s, Alksnis's grandfather, Yakov Alksnis () was the head of the Soviet Air Force.He also took part in the military tribunal for the Case of Trotskyist Anti-Soviet Military Organization, which sentenced Mikhail Tukhachevsky and other high-ranking Soviet officers to death on Joseph Stalin's order.However, only eight months later, Yakov Alksnis himself was also arrested and executed.