1996: three-year-old season

Zagreb did not race as a two-year-old in 1995 and made his debut in a ten furlong maiden race at the Curragh on 13 April 1996. Ridden by Mick Kinane, he started favourite against twenty-six opponents and won by a length from the Aga Khan's colt Sharazan.^[5] On his second appearance, the colt was matched against older horses in the Quality Beef Stakes over one and a half miles at Leopardstown Racecourse on 12 June. He started 4/7 favourite but finished second of the eight runners, beaten a head by Damancher, a four-year-old colt who had lost all of his previous thirteen races.^[6] Pat Shanahan took over the ride when Zagreb started a 20/1 outsider for the Irish Derby at the Curragh eighteen days later. The betting was headed by the Henry Cecil-trained Dushyantor, who had finished second when favourite for The Derby, with the other leading contenders including the 1995 Cartier Champion Two-year-old Colt Alhaarth, the previously undefeated Dr Massini (ridden by Kinane) and the Grand Prix de Saint-Cloud winner Polaris Flight who had been beaten a nose in the Prix du Jockey Club on his previous start. Shanahan settled Zagreb just behind the leaders before turning into the straight in third place behind Private Song and Dusyantor, with Polaris Flight close behind. Zagreb took the lead two furlongs out and was never in any danger of defeat, accelerating away from the field to win by six lengths from Polaris Flight, with another six lengths back to the Aidan O'Brien-trained His Excellence in third.^[7] Immediately after the race Shanahan commented "We have always thought a lot of him. I expected Zagreb to run well and I thought he would finish in the first four or five".^[8] When asked about his victory eighteen years later, the jockey admitted "What do I recall of the race? Not a lot is the answer - and I don't remember much about the following week either!"^[9]

After a break of more than three months, Zagreb returned for France's most prestigious race, the Prix de l'Arc de Triomphe over 2400 metres at Longchamp Racecourse on 6 October. Re-united with Kinane, he started the 6.6/1 third choice in the betting behind Helissio and Swain. Zagreb pulled against Kinane's attempts to restrain him in the early stages, but turned into the straight in third place and maintained his position until the field approached the last 200 metres, but then dropped back quickly and finished thirteenth of the sixteen runners, fourteen lengths behind the winner Helissio.^[10]