"Self-rule" referendums have been held in Ukraine's easternmost areas, with pro-Russian separatists claiming nearly 90% voted in favour in Donetsk region.
BBC reporters at polling stations in Donetsk and Luhansk regions spoke of chaotic scenes, no voting booths in places and no electoral register.
At least one person is reported to have been killed by armed men loyal to Ukraine's government.
Ukraine called the vote a "criminal farce" organised by Russia.
Western countries have also condemned the vote. Separatist leaders ignored a call by the Russian president to delay it.
The head of the self-proclaimed Donetsk People's Republic election commission Roman Lyagin told journalists that 89% voted in favour of self-rule, with 10% against, on a turnout of nearly 75%.
There are no results from the Luhansk area so far.
A Donetsk separatist leader, Denis Pushilin, told one Russian news agency that once the results are announced, all Ukrainian military troops in the region would be considered "occupying forces".
The shooting incident, in which separatist officials said at least one person had been killed, took place in Krasnoarmiisk, west of Donetsk city, after armed men supporting the Kiev government closed down a polling station.
A photographer with AP news agency reported seeing two people lying motionless on the ground.
A few hours before polling was due to close, separatist officials claimed turnout in Donetsk region had been close to 70% - but there was no independent confirmation. In other developments:
- An official at a Sloviansk polling station told the BBC voting was going well. Pro-Russia militiamen in fatigues and balaclavas were voting alongside grandmothers
- But one pro-Ukraine teacher said she received death threats after refusing to let rebels use her school as a polling station
- In Donetsk, the BBC's Piers Schofield says the process appears haphazard. Although there are voters' lists in polling stations, one can vote at any station
- BBC reporters say only a handful of polling stations are serving Mariupol, a city of half a million.
The ballot papers in Ukrainian and Russian ask one question: "Do you support the Act of State Self-rule of the Donetsk People's Republic/Luhansk People's Republic?"
A second round of voting is planned in a week's time, on joining Russia. Organisers also say they will boycott Ukraine's presidential elections on 25 May.
Ukraine's interim President Olexandr Turchynov has admitted many in the east supported pro-Russian militants, but warned the referendums were "a step towards the abyss".
The EU and US have also condemned the referendums, amid fears Ukraine could be sliding to civil war.
A Pew Research Centre survey suggested a majority even in eastern Ukraine - 70% - wanted to remain in a united country, despite concerns about governance.
Russia annexed Ukraine's southern autonomous republic of Crimea after a March referendum.
Bill Taylor, a former US ambassador to Ukraine, said results from Sunday's vote should be treated with caution after what happened in Crimea.
Russia is estimated to have some 40,000 troops near the border and says they have been pulled back, but Nato says it has seen no sign of this.
EU leaders have warned Russia it faces further sanctions if Ukraine's presidential election fails to go ahead.