Olsen, 49, had been in charge of Holland's most successful club of the Nineties for only 18 months. In his first year in charge he led Ajax to a domestic league and cup double but success in European competitions eluded the club. The four-time European champions finished last in Champions' League Group A and did not win a European tie away from home under the Dane.
Jan Wouters, a former Ajax player and Dutch international, will succeed Olsen. Wouters, who formerly trained Ajax's reserves, has signed a contract with Ajax until June 2002.
Olsen made a record 102 appearances for Denmark and captained his national side at the European Championship in France in 1984 and at the World Cup in Mexico in 1986. After ending his playing career, he turned to training but was fired by Danish club Brondby and Germany's FC Cologne.
After signing a two-year contract in January 1997, Olsen pledged to continue Ajax's trademark attacking style of football, but in recent weeks the club, plagued by injuries to key players, have struggled for form. The club at present lies third in the Dutch league, nine points adrift of leaders and arch rivals, Feyernoord of Rotterdam.
Meanwhile, one of this afternoon's Premiership matches sees Gerard Houllier's under-achieving Liverpool, who have lost seven of their last 10 games, take on Joe Kinnear's high-flying Wimbledon. "It is a match for people who have got some character and some guts. It will be a fight, a tough game," said Houllier yesterday.
The other match features two clubs who, despite struggling of late, have maintained their challenge for the title. Aston Villa, leaders for most of the season so far, take on last year's champions, Arsenal, in a match which neither team can afford to lose. Dennis Bergkamp is set to return, adding much-needed firepower to the Arsenal front line, while Villa's Paul Merson is doubtful with a back injury.
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