Bosnia, through its mainly Muslim wartime presidency, filed the case 13 years ago accusing Belgrade of committing genocide against the non-Serb population of Bosnia during the bloody war that was raging there, and demanding compensation.
The Bosnian war, which lasted from 1992 to 1995, claimed up to 200,000 lives and left millions of refugees homeless.
Observers say that Bosnia faces a huge challenge when it starts presenting its case on Monday, as most of the documented horrors of the war were committed by Bosnian Serb troops.
Serbia was not officially involved with the war, although there had been evidence before the UN war crimes court for the former Yugoslavia that Belgrade supported the wartime Bosnian Serb leadership financially and strategically.
Janet Anderson, an international justice expert for the Institute of War and Peace Reporting, asked: "To what extent can Bosnia prove that Serbia was involved and how do you judge the role of another state in a war by proxy?"
Bosnia's legal team will rely on evidence gathered by prosecutors in earlier cases at the International Criminal Tribunal for the former Yugoslavia (ICTY) and is expected to focus on the 1995 Srebrenica massacre of about 8000 Muslims by Bosnian Serb troops led by top war crimes fugitive Ratko Mladic. It is the only episode in the 1990s Balkan wars deemed by that tribunal to have constituted genocide.
The ongoing trial of Slobodan Milosevic, the former Yugoslav president, will also play a key role in the Bosnian case. The prosecutor has tried to show that Belgrade controlled and supported the Bosnian Serb leadership,
Most of the war crimes were
committed by Bosnian Serbs
Dutch attorney Phon van den Biesen, who is representing Bosnia before the court, told AFP: "We will look at the financial structures, who kept the Bosnian Serb entity in Bosnia afloat. We think a picture will emerge that the Federal Republic of Yugoslavia (since renamed Serbia-Montenegro) was the motor behind what happened in Bosnia."
Serbia-Montenegro for its part is expected to repeat its argument that the ICJ has no jurisdiction to deal with Bosnia's claim, as the Federal Republic of Yugoslavia (FRY) - replaced in 2003 by the loose union of Serbia and Montenegro - only became a member of the UN in 2000.
A problem with this argument is that the court already threw it out in preliminary hearings in 2002.
If Belgrade's jurisdiction arguments fail and Bosnia comes up with documents linking Belgrade to the Srebrenica massacre, it is expected to argue that Bosnia cannot show intent to commit the crime on the side of the Serb state.
"To what extent can Bosnia prove that Serbia was involved and how do you judge the role of another state in a war by proxy?"
international justice expert
"The crucial thing for genocide is that you have to show a special kind of intent to implement genocide," Anderson said.
Before the hearings, a member of Belgrade's legal team, Radoslav Stojanovic, said: "Maybe there were individuals who had intentions to destroy the Muslim people in Bosnia and they should be tried, but nobody could prove that such an intention towards Muslim people existed in FRY."
The hearings start on Monday at the Peace Palace in The Hague, with Bosnia presenting its case at 0900 GMT. The case will take over two months, ending on 9 May when the 16-judge panel will retreat to consider a verdict, something that typically takes months.
All rulings by the ICJ are final and without appeal, although the court has no means to enforce decisions.