In 1993 he finished equal first (with Viswanathan Anand) in the Groningen tournament to determine challengers for the Professional Chess Association World Championship title. This took him to the knock-out stage, where he beat Sergei Tiviakov in the first round, but lost to Anand in the second. In 1994 he played in the Candidates of the FIDE World Championship, losing to Boris Gelfand in the first round.
In 1997, he took part in the FIDE World Championship, which, for the first time, was a large knock-out event, the winner of which would play a match against reigning champion, Anatoly Karpov. This tournament included most of the world's top players (Gary Kasparov, Vladimir Kramnik and Gata Kamsky were the only notable absentees), and Adams won short matches against Tamaz Giorgadze, Sergei Tiviakov, Peter Svidler, Loek van Wely, Nigel Short, before coming up against Anand in the final round. Their four games at normal time controls were all drawn, as were four rapidplay games at quicker time limits, before Anand won the sudden-death game, knocking Adams out.
Among his other notable results are joint first at Dos Hermanas in 1995 (with Kamsky and Karpov), joint first at Dortmund in 1998 (with Kramnik and Svidler), and clear first at Dos Hermanas in 1999, ahead of Kramnik, Anand, Svidler, Karpov, Veselin Topalov, Judit Polgar and others.