Voting at more than 8,600 polling stations, including 295 in Kosovo, begins at 7am on Sunday and ends 13 hours later.
The first preliminary estimates are expected at about 20:00 GMT.
Elections were called when the government crumbled in March after most members of the European Union recognised Kosovo.
Vojislav Kostunica, the Serbian prime minister who like the Radicals favours closer ties with Russia, has made the battle to keep Kosovo in Serbia the cornerstone of his re-election bid.
Vojislav Seselj, the Radicals' formal leader, is an old Milosevic ally who is being tried for war crimes before the UN's international criminal tribunal for the former Yugoslavia (ICTY) in The Hague.
Tomislav Nikolic, the party's acting leader, hopes to join forces with Kostunica's Democratic Party of Serbia which has yet to rule out such an option.
Running on the ticket "For a European Serbia", Boris Tadic, the Serbian president and leader of his pro-Western Democratic Party, runs a close race with the nationalist Radical Party.
Each camp is expected to pick up at least one-third of the vote.
Aleksander Popovic, a Serbia government minister, told Al Jazeera: "Our relations with certain countries will depend not only on our wishes, [they] will also depend on the attitude of these countries towards the territorial sovereignty and integrity of Serbia".
Given the tightness of the race, the two main blocs, the pro-Europeans and nationalists, will need to produce a coalition with at least one other smaller party.
Analysts have been busy predicting possible coalitions, mostly coupling the Radicals with Kostunica's nationalists, or Tadic's Democrats with those representing minorities.
The creation of a nationalist government is certain to end Belgrade's co-operation with the ICTY, thus halting its integration with the European Union and pushing it back into the isolation of the 1990s Milosevic regime.
In a move meant to woo voters disillusioned with the West, the EU signed last week a pre-membership pact with Serbia.
However, this only added to a campaign that was marred by death threats against Tadic.
The parliamentary and local polls will be held in Kosovo despite opposition from the UN and Kosovo's ethnic Albanians about the local elections, which they see as an attempt by Serbia to partition the breakaway territory.
Some 40 nations including the US and all but a handful from the EU have recognised Kosovo since its ethnic Albanian-dominated parliament unilaterally declared independence on February 17.
The loss of the southern territory, viewed by most Serbs as the cradle of their history, culture and Orthodox Christian religion, has buoyed support for the nationalists in the run-up to the elections.
Source: Al Jazeera and agencies