Bečvář, who started for the Dukla Liberec , appeared internationally for the first time at the 1980 Winter Olympics in Lake Placid . There he took 44th place over 15 km, 32nd place over 30 km and ninth place with the relay. In the 1981/82 season he achieved eighth place in Brusson over 30 km and second place in Castelrotto over 15 km, 23rd place in the overall World Cup and thus achieved his best overall placement. In addition, with this second place he achieved his only podium finish in the individual World Cup. At the season highlight, the 1982 World Championships in Oslo , he came in 38th place over 30 km, 36th place over 15 km and 22nd place over 50 km. At the 1984 Winter Olympics in Sarajevo , he finished 29th over 15 km, 27th place over 30 km and 23rd place over 50 km. In the following year he ran at the world championships in Seefeld in Tyrol on 51st place over 15 km, 26th place over 30 km and fifth place over 50 km. He was also there together with Milan Blaško , Pavel Benc and Petr Lisičan eighth in the season. Two years later he came at the world championships in Oberstdorf on the 27th place over 15 km classic, on the 25th place over 30 km classic and together with Ladislav Švanda , Petr Lisičan and Pavel Benc on the fourth place with the relay. In January 1988 he was third with the relay at the World Cup in Štrbské Pleso .
At the Czechoslovak Championships Bečvář won four times over 30 km (1983, 1984, 1986, 1987), three times with the relay of Dukla Liberec (1983, 1986, 1988), twice over 50 km (1981, 1985) and once over 15 km ( 1984).
Czechoslovakia