Alekseev was the captain of the senior Soviet Union national basketball team.

He played with the USSR at the EuroBasket 1947, where he won a gold medal, and averaged 10.2 points per game.

He also worked as an assistant coach of the senior Soviet Union national basketball team.

He was an assistant coach on the Soviet Union team that won a silver medal at the 1960 Summer Olympics.

He was also an assistant coach with the Soviet Union, when they won the gold medal at the EuroBasket 1961.