A ruling by the court in favor of Yushchenko -- who says the runoff was fraudulent -- could boost the opposition's call for a new vote.
A ruling in favor of Yanukovych would clear the way for the prime minister's inauguration as president.
Yushchenko ally Yuliya Tymoshenko has urged opposition supporters to mass outside the Supreme Court today while it hears the case.
Tens of thousands of pro-Yushchenko supporters have been gathering peacefully daily in Kyiv's Independence Square since the 21 November runoff.
A regional council in in the Donbas coal-mining region voted overwhelmingly on 28 November to stage a referendum
on greater autonomy from the capital Kyiv on 15 December, prompting fears that the electoral impasse could lead to serious efforts to divide the country.
Outgoing President Leonid Kuchma, who backed Yanukovych in the run-up to the presidential election and has referred disparagingly to the opposition protests, said of local calls for possible referendums on autonomy: "We can't in any instance allow the disintegration or split of Ukraine."
The European Union and NATO both called for Ukrainian unity today in light of the calls for a referendum on splitting the country into eastern and western halves.
EU High Representative for Common Foreign and Security Policy Javier Solana said "the unity of Ukraine is fundamental."
The Ukrainian parliament's declaration on 27 November that the election was flawed won support from 255 of the 429 legislators present. Significantly, the parliament also passed a vote of no confidence in the Central Election Commission that declared Vanukovych the winner.
Although the resolution is nonbinding, it increased hope among Yushchenko's supporters that the final round of the election might be conducted again.
Meanwhile, the Ukrainian National Bank head who also headed Yanukovych's campaign for president, Serhiy Tyhypko, announced at a news conference today that he is resigning from the central bank to concentrate his efforts on Yanukovych's political efforts. Tyhypko also serves as chairman of the Labor Ukraine Party. It was not immediately clear what the consequences will be of Tyhypko's resignation.
(Reuters/AFP)[Click here to see RFE/RL's continuing coverage of Ukraine's disputed election.]