Bevrid drove in the 1992 DTM , in which he started with his own team in a privately entered BMW from his home race in Brno. In 1993 he drove in the DTM for the entire season. In 1994 he switched to the Belgian Touring Car Championship. He also drove in the German Super Touring Car Cup in 1994 and took part in the FIA Touring Car World Cup. He also took part in this in 1995. He also competed in the Czech Touring Car Championship in 1995 and was third in the overall standings. In 1996 he remained loyal to this series and improved to 2nd overall. In 1997 he switched to the Central European Super Touring Car Championship and was runner-up straight away. In 1998 he stayed true to this series and finished sixth overall.