At the age of 18, Alekseyev began practicing weightlifting at Trud VSS, trained by his coach Rudolf Plyukfelder until 1968, when he began to train solo. He was not a naturally large man like other super heavyweights but was encouraged to gain strength by adding weight. In January 1970 Alekseyev set his first world record, and during the World Weightlifting Championship in Columbus, Ohio, US. In 1970 he was the first man to clean and jerk 500 pounds (227 kg) in competition. During one of his early world records, Oscar State OBE remarked that the weight of over 460 pounds (209 kg) in the Olympic press looked so easy it could have been a broomstick. This was the beginning of a series of 80 world records Alekseyev set between 1970 and 1977. He received bonus funds by the Soviet government every time he set a world record (Soviet athletics were funded by the state); so he made it a point to gradually increase his world records by 1.1 pounds or 0.5 kg. He was unbeaten and held the World Championship and European Championship titles for those eight years. He was the first man to total over 600 kg in the triple event.