The group of seven, who were travellig to Venice on a trip organized by the Italian Association for Down's Syndrome People (AIPD), had queued for tickets at Conegliano station, in the northern region of Veneto.
But when they reached the ticket-desk, a member of staff told them they were too slow and would have wait for the next train.
Eliana Pin, a teacher at the association which organized the trip told The Local that the group had purposefully arrived early to allow them time to buy the tickets.
“They'd got there half an hour before the train arrived, but the person in front of them in the queue didn't speak good Italian and took a long time to get his ticket.
“So by the time it was their turn, there were just ten minutes left before the train arrived.”
The group, who are aged between 24 and 31, had to wait almost two hours for the next train.
Later that day, at the station in Mestre, they yet again had difficulty buying tickets.
One member of the group had asked correctly for two tickets to Venice. But the ticket seller turned to the teacher standing behind the group, saying: “I can't stay here and waste time. I have more experience than you. They aren't capable of learning anything.”
The woman then explained that it was important for the group to be able to buy their own tickets because it encouraged them to be independent, which they had been for years.
Pin said that the man then told the teacher: “Do your community a favour and get the tickets for them.”
To avoid an upsetting row, the teacher ended up buying the tickets herself.
“In the end, the group had a good weekend," said Pin. "But when they all came home, the first thing they told their families was what had happened at the stations.
"We've never had problems with ticket offices before. And to have it happen twice in one day has made us really angry.”
Both incidents have been strongly criticized by the association, which has accused Italian train operator Trenitalia of discrimination.
Responding to the accusations, Trenitalia said: “If the details will confirm such disrespectful and offensive attitudes we will not fail to impose sanctions, as set out by our internal rules.”
The charity also told The Local it had received a personal apology from the regional director of Trenitalia, who invited them to a meeting to help raise awareness about the issue.