With four hours of voting to go, Greeks are turning out in solid numbers to vote on their financial future.
Private Mega TV channel says turnout has been markedly high, now standing at 35 percent, and lines have been seen at polling stations in Athens.
Turnout must be above 40 percent for the referendum to be valid.
High turnouts are normal in Greece because voting is mandatory — although that law has not been enforced in recent years.
In the country's first referendum since 1974, Greece's 9.8 million voters are choosing Sunday whether to accept demands by international creditors for more austerity measures in return for bailout loans.
Greece voted in a tightly fought referendum Sunday that Prime Minister Alexis Tsipras said will determine its "destiny" in the eurozone, as the EU country teetered on the brink of financial collapse.
From remote Aegean islands to the shadow of the 2,400-year-old Parthenon in Athens, Greeks despairing at years of austerity -- and angry at capital controls this week that have closed banks and prompted a clean-out of supermarket shelves -- cast their ballots.
Polls show opinion evenly divided between 'Yes' and 'No' with many believing neither result would provide a quick and clear solution to Greece's debt woes.
Fear that a 'No' result urged by the government could put Greece on the path to an exit from the eurozone -- a so-called Grexit -- spooked some.
"When you have to choose between two bad solutions, you choose the least bad, and that's clearly 'Yes'," said Dimitris Kavouklis, 42, as he voted in an upmarket district of the capital.
But Dimitris Halatsis, a teacher, said on such a "crucial day" he was voting 'No' because "it's the only chance the government and Greece have to apply pressure" on its international creditors.
Tsipras said he was confident of a 'No' as he voted in his northern Athens neighbourhood, saying that would force concessions from the creditors to give Greeks less austerity and more "dignity".
"No one can ignore the will of the people to live, to live with determination, to take its destiny into its own hands," he said, appearing relaxed and wearing an open-necked white shirt.
Tsipras's flamboyant finance minister, Yanis Varoufakis, has accused Athens's creditors of "terrorism" for raising the spectre of Grexit. He insists no legal mechanism exists to make it drop out of what is meant to be an "irreversible" monetary union.
Varoufakis has vowed to resign if a 'Yes' prevails, and the pressure would be on Tsipras to do the same.
Voting was to close at 7:00pm (1600 GMT), with results expected a couple of hours later.
Even though many grumbled that the long and technical question they were voting on was impossible to understand, minds for the most part were made up.
Michelis, an 80-year-old first through the doors of a primary school being used for the vote in central Athens, said he too was saying 'No' "because they (the creditors) will take us more seriously".
Theodora, 61, a retired journalist, said she was voting 'Yes' because "it's a 'Yes' to the European Union".
In the largely middle-class Pangrati neighbourhood, voter turnout was high, with even the very elderly making their way determinedly up a flight of 40 steps to reach polling booths.
Summing up the uncertainty felt by around one in 10 Greek voters, 56-year old Katerina had still not made up her mind which way to vote, even as she collected her ballot paper.
"It is very confusing, it's very hard, not at all easy to decide," she said, admitting that she had voted to elect Tsipras but was disappointed by his failure to strike a deal with the country's creditors.
Greece was officially declared in default on Friday by the European Financial Stability Facility, which holds 144.6 billion euros ($160 billion) of Greek loans, days after becoming the first developed country to miss a debt payment to the International Monetary Fund.
With its credit lifeline reduced to a trickle, the government this week closed banks and capped daily ATM withdrawals to 60 euros ($67).
The banks' liquidity was expected to dry up entirely within days unless the European Central Bank (ECB) -- a major creditor -- injected funds quickly.
Tsipras has called for the ECB, IMF and European Commission to forgive 30 percent of the 240 billion euros ($267 billion) they have loaned Greece over the past five years and allow it a 20-year grace period before it starts repaying the rest.
So far, the German government led by Chancellor Angela Merkel has been playing hardball with Greece. Some reports suggested it wants to force a Grexit as a lesson to other lagging eurozone nations.
But that was causing a split among the big eurozone economies.
In an interview published Sunday, Italian Prime Minister Matteo Renzi said that, no matter the referendum's result, "we must start talking to each other again -- no one knows that more than Angela Merkel".
France's economy minister, Emmanuel Macron, said that even if Tsipras gets his 'No', bailout talks must resume. And in what could be seen as a thinly-veiled jibe at Germany, he warned that Europe cannot "crush an entire people".