The International Court of Justice in The Hague must decide whether Croatia or Serbia -- or both - are guilty of genocide during the Croatian 1991 - 95 independence war.
Croatia wants the Court to rule that Serbia committed genocide across the country but especially in the eastern city of Vukovar in 1991.
It accuses the Belgrade authorities of ethnic cleansing against some 20,000 Croatian citizens, particularly in Vukovar where fighting was heaviest.
The Croatian legal team said it hoped the trial would shed light on the fate of almost 1,700 people still missing.
They're believed to have been killed and buried in mass graves byYugoslav forces.
(SOUNDBITE) (English) CROATIAN LEGAL REPRESENTATIVE VESNA CRNIC-GROTIC SAYING:
"The 1948 Convention aimed at preventing and outlawing actions of the kind that were taken on the territory of Croatia. Beginning in the summer of 1990, it started with unrest and instability in the areas where the Serbs lived, but grew gradually to the genocidal campaign incited, organised, controlled and facilitated by the respondent."
But Serbia has filed a counter claim over the expulsion of 230,000 Serbs from Croatia in 1995.
The head of Serbia's legal team said on Sunday crimes committed did not have "the characteristics of genocide".
(SOUNDBITE) (English) SERBIAN LEGAL REPRESENTATIVE SASA OBRADOVIC SAYING:
"I think that we have strong arguments, that we have convincible evidence that what's happened in Croatia, of course, horrific crimes were happened, were committed in Croatia and it should not be forgotten, but those crimes didn't fulfil the legal requirements, legal elements of the crime of genocide."
The Croatian team will spend this week presenting its arguments before the Serbian counter-claim next week.
A binding ruling is expected here either late this year or in early 2015.