Clackmannanshire in central Scotland was the first to have announced the results of Thursday's independence referendum: 46% for and 54% against it, the local authorities said on Friday, ITAR-TASS reported.
Almost 40,000 voters were eligible to vote in the district; the turnout was 89%
Vote counting is in progress in all the other districts.
BBC said such high turnout might signify that it would take longer for the final results to be announced.
Initially, it was planned that the official figures would become known by 08:00 local time Friday.
At first, the tellers will count the total number of ballots cast and then the votes themselves.
According to the YouGov public opinion service, 54% of people who came to the polling stations voted against independence and 46% for it.
Its earlier poll published on September 6 made quite a sensation with 51% of people favouring secession from the United Kingdom and 49% being against it.
No exit polls were conducted for reasons of costs and inaccuracy.
If Scotland votes for independence, it will be declared on March 24, 2016. Until then, Edinburgh and London will have to agree on the terms of secession.
The final results are expected to be announced on Friday morning or afternoon. Local television channels will be reporting current results throughout the night in all 32 districts.
With a hypothetical 100% turnout, it will take about 2.1 million votes for Scotland to break away from Great Britain. Of the record large electorate of 4.3 million people, about 790,000 preferred to vote by mail.
The authorities expect a turnout of about 80% In this case, some 1.72 million "yes" votes (provided there are no spoiled ballots) will need to be cast for Scotland to become independent. Only the absolute number of votes cast will be taken into account.
Queen Elizabeth II, who is closely watching the referendum from its Balmoral Castle in central Scotland, will hold a special meeting with her close adivers after the results have been announced, her representative said.
The monarch will unquestionably accept any outcome of the referendum, BBC quoted one of the queen's closest aides as saying.
Queen Elizabeth will retain the title of formal head of state if Scotland secedes from the United Kingdom. She has not made any official statements on the plebiscite but expressed hope on Sunday that people would think well about their future before voting for or against Scotland's independence.
England and Scotland united under the Act of Union of in 1707. Prior to that, for about a hundred years, they had one king but different system of government.