Moldovans are voting in a parliamentary election, three months after a disputed ballot led to violence and two deaths, BBC reported.
The opposition has been demanding a re-run of April's election, claiming it was rigged.
The new vote is being held because the Communists, who won a majority in the initial poll, failed to win enough seats to elect a president.
Opposition parties boycotted the votes to elect a replacement for outgoing President Vladimir Voronin.
Polling stations opened at 0400 GMT and are due to close at 1800 GMT.
After the April result, thousands of people took to the streets, clashing with police, and storming parliament and the presidential offices.
The opposition and some international observers said the vote had been rigged, although others said it was generally fair.
The Communist Party gained 60 of the 101 seats - one short of the 61 seats needed to meet the three-fifths majority required to elect its presidential candidate, current Prime Minister Zinaida Greceanii.
Opinion polls this month suggested a drop in support for the Communists.
In Wednesday's vote, three opposition parties hope to join the Communist Party in parliament - the Liberal Party, the Liberal Democratic Party and the Our Moldova Alliance.
They have pledged to create a ruling coalition if they collectively gain enough votes.
They have also said that they will co-operate with the Communist Party in the new parliament if the "early election is fair, democratic and transparent".
Mr Voronin's successor will lead the poorest country in Europe - where the average wage is just under $250 (£151) a month - and will inherit an unresolved conflict over the breakaway region of Trans-Dniester.