It looks as though the SNP has done well. With just over 2% of the votes cast, the SNP is getting around one-third of the ministries, including finance and defence.
Yugoslavia's new government includes a strong Montenegrin contingent made up of long-standing supporters of the ousted Yugoslav leader, Slobodan Milosevic, not least among them the prime minister-designate.
Mr Kostunica's alliance, the Democratic Opposition of Serbia (DOS), emerged as the strongest group in September's presidential elections, but failed to get an outright majority.
In any case, it was obliged to bring Montenegrin representatives into the coalition.
SNP success
The process of forming a government was further complicated by the fact that virtually all the 50 places reserved for Montenegro in the 178-seat federal parliament were won by the previously pro-Milosevic Socialist People's Party of Montenegro (SNP).
The SNP - which is in opposition in Montenegro - owed its overwhelming success to the Montenegrin governing coalition's boycott of the Yugoslav elections.
That boycott had been prompted by the constitutional amendments Mr Milosevic had earlier forced through which Montenegro considered illegitimate.
It did not take too long for the SNP to abandon Mr Milosevic after a revolt in Belgrade finished him off politically.
But the SNP has fought hard to get a good share of government portfolios and it has also insisted on a minor party from Montenegro gaining one ministry.
It looks as though the SNP has done well. With just over 2% of the votes cast, the SNP is getting around one-third of the ministries, including finance and defence.
That includes the prime minister's post - given to SNP's deputy chairman Zoran Zizic - which by convention goes to a Montenegrin when the presidency is held by a Serb.
DOS ministries
On the Serbian side, the DOS gets all the 10 ministries.
Some of its most prominent representatives include the man tipped to be foreign minister, Goran Svilanovic, who this week attended his country's admission into the United Nations in New York.
A long-standing human rights activist, he leads the Civic Alliance - one of the few Serbian parties that has eschewed nationalism.
Economics professor Miroslav Labus is set to become deputy prime minister and will oversee Yugoslavia's foreign economic relations.
Belgrade is desperate to revive trade, attract aid and lure investment to the country.
State power
The inauguration of a new government will speed up Yugoslavia's return from semi-pariah status to full membership of the international community.
But in many ways, the key decisions lie not with the federal government but with the republican administrations in Serbia and in its increasingly estranged partner, Montenegro.
And those governments of the two constituent states of Yugoslavia represent a further headache for the central administration.
Montenegro is expected to hold a referendum by next June on its relations with Serbia which could lead to its independence.
Early elections are scheduled in Serbia for December.