 At the peak of his career, Ribli was twice a candidate for the World Championship, in 1984 and 1986.At London in 1984, he participated in the high-profile match between USSR and the Rest of the World, defeating his Soviet counterpart, Rafael Vaganian by a narrow margin.In 1983, Ribli defeated Torre (+3-1=6) in Quarter Final Candidate Match, but lost to Smyslov (+1-3=7) in Semi-Final.