Even with the limit, many ATMs ran out of money.
And, despite the bank closures, some pensioners formed lines outside the banks in the hope that they might open.
"I don't have a card, I don't know what's going on. We don't even have enough money to buy bread," Anastasios Gevelidis, 74, told the Associated Press. He had arrived outside a bank in Thessaloniki at 4 a.m.
The chaos wasn't limited to the banks, either: Many retailers had decided to stop accepting credit card transactions by Monday.
There were also some signs of panic-buying at gas stations and supermarkets.
The Greek stock and bond markets also were closed Monday. They are due to be reopened next week.
All of this is happening in front of the world's reporters, many of whom have flown in to cover the crisis. "Savers are being mobbed by journalists from around the world looking for juicy quotes," Business Insider's Mike Bird reported from Athens on Monday.
Greece is due to hold a referendum on Sunday on whether the country should accept the tough austerity terms its creditors want. If the "no" vote wins, Greece may be forced to leave the euro zone, and some experts worry that the country could face a humanitarian crisis.
However, Prime Minister Alexis Tsipras was elected on an anti-austerity ticket, and his leftist Syriza party is campaigning for a "no" vote. There are signs in Greece that many support him.
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