Dragan Stojkovic (L) and Ilija Petkovic
According to Serbia's leading newspaper, Stojkovic and Petkovic quit after a string of disappointing results culminating in the team's failure to qualify for the 2002 World Cup and Euro 2004 finals.
Stojkovic and Petkovic were not immediately available for comment but the daily quoted them as saying it was time for others to take over after a long barren spell.
"I am not a quitter. I've always walked tall and I will continue to do so but my feeling is that I can no longer perform this duty capably and take our soccer back to winning ways," Stojkovic was quoted as saying.
Petkovic said he decided to end his second spell in charge "for the national team's sake".
"The national team is sacred to me like my family and the future of our football is more important than my own. This is a very painful decision but I believe it's for the best," he said.
Petkovic took over from Dejan Savicevic in the closing stages of the team's unsuccessful Euro 2004 qualifying campaign after a shock 2-1 defeat to Azerbaijan that effectively buried Serbia-Montenegro's hopes of reaching the finals.
Serbia and Montenegro were held to a 1-1 draw in a friendly against Slovenia on Wednesday, the last warm up for their 2006 World Cup qualifying campaign which begins against San Marino on September 4.
Many fans called for radical changes within the FSSCG after the Olympic football team's disastrous performances in Athens, where they lost 6-0 to Argentina, 5-1 to Australia and 3-2 to Tunisia.