When I read "he is quite famous in Serbia" I thought to have a look if there is a wikipedia article in the Serbian wikipedia. And bingo, there is. He's actually quite an interesting person, among others he is the founder of the Serbian Olympic Comittee in 1910. (Then it was named "Serbian Olympic Club".) He was the Head of Delegation during the Olympic Games of Stockholm in 1912, when he was also elected as member of the International Olympic Commitee, a seat he held until 1949 when he withdrew of that. He also lead the Yugoslav Olympic delegations in Antwerpen 1920, Paris 1924, Amsterdam 1928 and Berlin 1936.
Militarywise he was participant of the Balcan wars from 1912 and 1913 and also in WWI and WWII. During WWI he participated in the liberation of Zemun, which is today a part of Belgrade, but until the end of WWII belonged to Austria-Hungary, because it's on the other side of the Sava River.
Also interesting is the fact that Svetomir died in Duisburg, Germany in 1960.
About his family in that wikipedia-article is written that his parents were father Svetozar and mother Draginja. His son is Dušan Djukić.
This is what I could find out via Wikipedia Serbia. I know it's not the way genealogy should be done, but it could give you a starting point from where to start.
Thanks for that, I learned quite a bit today.