Around 32 million of Russia's 110 million registered voters are eligible to vote in polls, which include elections for eight regional parliaments.
The elections come half way through President Dmitry Medvedev's four year term as he struggles to demonstrate progress on a pledge to loosen the tight control of the political system introduced during Vladimir Putin's eight years in the Kremlin.
Campaigning for Sunday's votes was marred by the barring of candidates from the liberal Yabloko party from two regional polls after officials ruled several thousand voter signatures required to get the party on the ballot were invalid.
Federal election officials have dismissed opposition complaints of bias and say Russian elections are more open than those in Western Europe.
However, Golos, Russia's largest independent election monitoring body, said there are few signs today's election will be fair or competitive.
Putin's United Russia is expected to dominate the elections, drawing on its immense resources, entrenched position and popular leader.
compiled from agency reports
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