In the first round on 14 April, turnout reached 55 percent, the lowest in any election since the former Yugoslav republic became independent 13 years ago.
In that vote, Prime Minister Branko Crvenkovski of the Social Democratic Union (SDSM) easily bested Sasko Kedev of the right-wing main opposition Internal Macedonian Revolutionary Organization (VMRO-DPMNE). Crvenkovski won some 42 percent of the vote to Kedev's 34 percent, but failed to win an outright majority.
Neither of the two ethnic Albanian candidates garnered enough votes to advance to the second round.
In their election campaigns, both Crvenkovski and Kedev appealed for a massive turnout today to avoid a prolonged power vacuum. If today's runoff fails, the election process will start from scratch.
The presidential post in Macedonia is largely ceremonial. Trajkovski -- a pro-Western, reformist president -- established his authority as a peacemaker by presiding over negotiations to end an armed conflict with ethnic Albanian rebels in 2001.
Both Crvenkovski and Kedev are vowing to pursue Trajkovski's goal of taking Macedonia into the European Union and NATO. The country submitted its formal application for EU membership in late March, one month after Trajkovski's death. Following in Trajkovski's footsteps, each of the two front-runners promises that, if elected, he will be a president "for all Macedonians."
Crvenkovski, a veteran politician, is pledging to work toward the full implementation of the Ohrid peace agreement, which ended months of clashes between security forces and ethnic Albanian rebels three years ago. Speaking at a pre-election rally over the weekend, Crvenkovski told supporters, "I expect you to trust me because I am convinced, because I am sure, because I know I will be a good president."
Kedev, a heart surgeon and a relative political novice, is promising a "new face" for Macedonia and is vowing to tackle widespread corruption and poverty.
Analysts say the votes of ethnic Albanians, who make up about one-quarter of the electorate, may be decisive. The ethnic Albanian Democratic Union for Integration (BDI), the SDSM's ally in the ruling coalition, is calling on its supporters to back Crvenkovski.
Kedev accused Crvenkovski of making a deal with the BDI, the party of former Albanian rebels, by promising them senior political posts if he wins. "Intense political negotiations, indecent political bargaining, is under way that will lead to constitutional changes, [that will lead] to giving key ministerial posts [to the ethnic Albanian BDI party]," Kedev said.
Both Crvenkovski's SDSM and the BDI deny any improper deal making. Refuting Kedev's accusations, an SDSM spokesman said, "[Those claims are the product of] an uneasy conscience, since all those things Kedev and the VMRO-DPMNE are now talking about are exactly the methods and the scenario they used while in power."
The second-largest ethnic Albanian party, the Democratic Party of Albanians (PDSH), says it will allow its supporters to decide for whom to vote.
The otherwise uneventful election campaign -- shortened to allow an early replacement for Trajkovski -- focused mainly on economic problems, especially the country's 36 percent unemployment rate.
European Union officials are strongly urging Macedonians to go to the polls. EU foreign policy chief Javier Solana, in an article printed in both Macedonian- and Albanian-language dailies, cautioned that failure of the runoff will mean a delay in urgently needed economic reforms and a "setback" on Macedonia's road toward the EU and NATO.
RFE/RL's correspondent in Skopje, Muhamed Zekiri, said voting is proceeding smoothly, with only one minor incident reported. "The election process [by noon today] is proceeding without any major problems. All 2,973 polling stations opened at 7 a.m. today, where more than 1.5 million citizens registered in election lists must cast their ballots," he said.
Voting ends at 7 p.m. (local and Prague time). First official results are expected tomorrow.