All 14 were arrested at Kalamata
Patrick Dirksen and Frank Mink are being held in poor prison conditions in deteriorating health and spirits, said Mr Dirksen's father Gert, an English teacher from Eindhoven.
Patrick, 27, has been coping well with his imprisonment, but the looming Christmas deadline and now poor health have brought increasing concerns about his mental state.
"As parents we have been very proud of the way he is coping, but we can hear from the tone of his voice that things are getting worse," Mr Dirksen told Online.
"They are there knowing they didn't do anything wrong, but he is definitely becoming more distressed because of the uncertainty.
"The level of stress is getting more and more a problem. His mental state is deteriorating. He is normally outgoing, social, an extrovert."
Student
Patrick, a 27-year-old geography student and part-time restaurant worker, had found the Greek trip advertised on the internet. He flew to Athens with his 28-year-old friend Frank Mink, from the town of Den Helder.
There they joined the British group, led by Paul Coppin. But the group's visit to Kalamata military base went disastrously wrong, when all 14 were arrested as spies.
"They were told the espionage charge could mean a 20-year prison sentence, and were shocked by that," said Mr Dirksen.
"It must be clear by now that there is no case. It is not a matter of espionage. We have even heard Greek security experts say: 'Send these people home - they are tourists'."
But as the legal battle continues, Gert Dirksen, his wife Trudy and Patrick's girlfriend are now devoting their lives to getting the men out.
Mr Dirksen says the men have been in danger of being the "forgotten" prisoners, overlooked in much UK coverage, and - initially - not making the headlines in the Netherlands either.
The Greeks are now under Dutch as well as British diplomatic pressure to ensure the men's release.
Dutch Foreign Minister Jozias Van Aartsen has been in contact with his Greek opposite number George Papandreou.
And the families are trying to ensure the matter will also be raised when Greek Prime Minister Costas Simitas visits Dutch Prime Minister Wim Kok next week.
Pressure from British MEPs has already apparently brought results.
"The conditions in prison are fairly primitive, but to start with they were sleeping on a mattress on a concrete floor.
"Now there have been some improvements, and they are in cells with the British prisoners."
But conditions remain difficult. For 18 hours a day the men are locked in their cells, and only brief phone calls to relative are possible.
Dutch popularity
Plane-spotting is a popular hobby in the Netherlands - unlike in Greece, where its cultural obscurity is seen as adding to the men's problems in proving their innocence.
So many Dutch plane-spotters attend military open days that special preview days are set aside for them, said Mr Dirksen.
Patrick had already been on foreign trips to the UK, Belgium, Germany and Sweden, but this was his first visit to Greece.
He speaks none of the language and knows little of the culture.
The idea that Patrick is a spy, is, says Mr Dirksen, absurd.
"From the very first moment we reacted with disbelief," he said.
"Nobody could believe there could be any truth in it. Spying is a ridiculous charge."
"If they are not out by 20 December, they will have to spend three weeks without anything happening," said Mr Dirksen.
"We have got nothing against Greece - we simply don't understand why this thing is going on and on."