Anatoly Alyabyev won his only Soviet title in 1979 in the 20 km and made his international début next year at the Olympic Winter Games, where he was very successful, medaling in all three biathlon events, winning gold in the 20 km and relay and bronze in the 10 km. At the World Championships Alyabyev won two bronzes, both in the relay in 1981 and 1982. He also won silver at the 1980-81 World Cup. After his sporting career he worked as a biathlon coach, coaching the Russian national team from 1990-98. Alyabyev graduated from the Military Institute of Physical Culture in Leningrad (1981), receiving a candidate degree in pedagogy in 1997. Since 1998 he has been a professor at his alma mater, publishing over 30 scientific papers.