Customers said they were left unable to buy tickets they had reserved after pages timed out as the site struggled to cope with demand for this year's shows.
Some saw their phone calls disconnected after being put on hold for an hour. Others were told to call back later, often after the tickets they were trying to book had sold out.
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Hide AdOne user told The Scotsman he had spent more than two and a half hours unsuccessfully trying to book tickets.
Other customers buying tickets for this year's event complained about being held up by Visa verification systems, with their tickets also being released due to the time delay.
The Fringe Box Office said in a statement that "quite a few people" had been affected by problems, but said it was a result of demand on the first day of sales.
Among the most popular tickets were those for free BBC shows featuring comedians such as David Mitchell and Ricky Gervais, and a special edition of radio show Just a Minute featuring Paul Merton and Nicholas Parsons.
Customers who missed out on those tickets are being advised to turn up at venues in the hope of spare seats being available.
There was chaos in the Fringe ticketing system two years ago, with shows oversold and customers left without tickets they had paid for.