After World War II he moved to Belgrade, achieving his first chess success in 1946, in the form of 2nd place in the championship of Yugoslav People's Army.
Nedeljković received the title of National master for his results in the individual finals of the Yugoslav Chess Championship in 1949 and 1950, while the title of International Master FIDE was awarded to him for winning the International Chess tournament in Belgrade in 1951.
In 1959, he shared the second place (behind Borislav Ivkov, together with Nikola Karaklajić and Sava Vuković) in Belgrade, and in 1961 for the second time in his career, he played for Yugoslavia in the European Team Chess Championship in Oberhausen, again winning the silver medal.
In 1947, Srećko Nedeljković was the founder of the Crvena Zvezda chess club in Belgrade, of which he was a lifelong member.
The legacy of Srećko Nedeljkovic includes 8 books, 212 scientific articles and 136 other documents related to medicine.