Kostic was vice president at the time of Yugoslavia's violent break-up in 1991 and 1992 and was the collective presidency's acting head for much of that time.
Kostić je bio potpredsednik u vreme nasilnog raspada Jugoslavije 1991 i 1992 godine, i vršilac dužnosti predsednika kolektivnog Predsedništva u većem delu tog perioda.