Zdravković initially practiced football as a youngster in Ćuprija, until a school teacher, Aleksandar "Aca" Petrović, suggested that he begin training athletics.[3] Zdravković's youth coaches emphasized gymnastics as a complement to his running workouts.[3] At the age of 21 he made his Olympic debut at the 1980 Summer Olympics. In the men's 1500 meters, he progressed through the qualifying heat and semi-final rounds, but finished last in the finals. In spite of this, he was particularly happy to race with Steve Ovett:
"Yes, Steve Ovett was more sympathetic to me than Sebastian Coe. Ovett was from a working family, but Coe was a Lord. In the Olympics final in Moscow they restricted warm ups on the training field, on the track only two strides were allowed before the race. I did my first stride and turned around. Ovett ran towards me, stopped next to me and offered his hand. I didn't want to wash it for four days from how happy I was. He was different, more natural." -Zdravković[4]
"I didn't have anything to lose, even if I was second it would have been a great result. Even today I joke about that race and say 'even the blind chicken gets some grain'. To be honest, if we ran three days later, he would have beat me." -Zdravković[4]
He had qualified for the 1984 Summer Olympics, but the Athletics Federation of Yugoslavia had a sportswear contract with Adidas, and after not changing his sportswear to Adidas, Zdravković was taken off the Yugoslavian 1984 Olympic team.[3]
