Pro-Russian separatists in Ukraine's two eastern regions are holding "self-rule" referendums - a move condemned by the Ukrainian government and the West.
BBC correspondents at polling stations report chaotic scenes, no voting booths and no electoral register.
Self-proclaimed leaders in the Donetsk and Luhansk regions are going ahead with the vote despite Russian President Vladimir Putin's call to postpone it.
Ukraine says the vote could result in the "self-destruction" of the regions.
Overnight, fighting was reported around the rebel-held city of Sloviansk, which remains sealed off by Ukrainian government troops conducting what they describe as an "anti-terror" operation.
One pro-Ukrainian head teacher told the BBC she was receiving death threats after having refused to let the rebels use her school as a polling station.
There is only one question on the ballot papers, in both Ukrainian and Russian: "Do you support the act of state self-rule of the Donetsk People's Republic/Luhansk People's Republic?"
The BBC's correspondent in Donetsk said the voting process appears haphazard. There are voters' lists in polling stations, but anyone can vote in any polling station.
The organisers have suggested they intend to hold a second round of voting later this month, on joining Russia. They also say they will boycott Ukraine's presidential elections on 25 May.
On Saturday, Ukraine's interim President Olexandr Turchynov admitted many in eastern Ukraine supported the pro-Russian militants, but warned that the referendums were "a step towards the abyss".
The EU and US have also condemned the referendums, amid fears that Ukraine could be sliding to civil war.