Conrad Clitheroe, 54, Gary Cooper, 45, and an unnamed friend were stopped by police for writing down aircraft registration numbers at Fujairah Airport.
Although plane spotting is not illegal in the United Arab Emirates, it is not understood and is frowned upon.
The men were taken to a police station, where they were allegedly told they could only leave if they signed a form in Arabic saying they would not practise their hobby there again.
But after signing the document, without asking for a translation, they were kept in custody overnight. They were brought before a prosecutor the next day and then moved to Fujairah Prison where they have been held for ten days.
