From 1966 Alekseyev lived in Shakhty, where in 1971 he graduated from the branch of the Novocherkassk Polytechnical Institute. He died on 25 November 2011 in Germany in a clinic where he had been sent for serious heart problems. He was 69. The Russian Weightlifting Federation reported his death and called him a "Soviet sports legend" and "one of the strongest people in the world". He was survived by wife Olimpiada and sons Sergey and Dmitry. Dmitry competed nationally in weightlifting, placing fourth at the 1988 Soviet weightlifting championships.