The polls are a prelude to general elections in December
Candidates backed by the Awami League party in Bangladesh have performed strongly in local elections, election commission officials say.
The party swept all four city corporations and eight of the nine municipalities that went to the polls.
The vote was a big step towards restoring democracy, said election commissioner Sohul Hussain.
General elections due last year were postponed after political violence and are now to be held in December.
Monday's voting took place in Sylhet, Khulna, Barisal and Rajshahi. Elections for the two other city corporations - Dhaka and Chittagong - and the rest of the country's more than 300 municipalities will be held by October.
Voting passed off without violence or vote rigging seen in the past.
Officially the candidates all have to be independent but some have been endorsed by different parties and so the results give an indication of their relative strengths.
Turn-out in the vote was high
Correspondents say the results prove the Awami League's grassroots strength and have left its traditional rival, the Bangladesh Nationalist Party, dazed.
In most of the key areas up for grabs, candidates linked to the Awami League triumphed.
They included Badaruddin Ahmed Kamran, the former mayor of Sylhet who is now in prison on corruption charges - he won a large sympathy vote to earn a second stint in power.
Early results released by the election commission on Tuesday also showed that Awami League candidate Talukder Abdul Khaleque clinched the mayoral race for Khulna City Corporation.
The party also performed well in the cities of Rajshahi and Barisal.
A local BNP leader won in just one municipality.
Emergency measures were relaxed in areas where voting took place and officials say the turn-out was high.
The BBC's Mark Dummett in Dhaka says that the peaceful nature of the vote will come as a huge relief to the government and the army, which staked their reputations on ensuring a credible transition to democracy.
The election commission says about 1.3 million voters - or 1.5% of Bangladesh's electorate - were eligible to take part in Monday's poll. They hope it will be a model for future ballots.
The government has promised to organise general elections by the end of the year.
But voting on Monday was not entirely smooth.
There were long delays because many voters and polling agents were confused by the new voter roll and identity system.