Passengers on the first of the new Caledonian Sleeper trains from Scotland to London arrived three hours late after signalling problems on the line.
The northbound service to Glasgow and Edinburgh was also delayed after being hit by what operators Serco called “teething problems”.
The signalling issue happened at Carstairs and led to the train not making it to London Euston until 10:30.
Serco has apologised to customers and offered them a full refund.
It said it would be be working with Network Rail to see why the issues occurred.
Sunday night’s debut services were part of a month-long “soft launch” of the new £150m fleet of trains.
Caledonian Sleeper’s managing director Ryan Flaherty said: “We had planned for everything last night but it was one of those things that was out of our control.
“Obviously we were very sorry for the guests that it impacted and they arrived late at their destination this morning.
“But actually we are very pleased with how the new trains operated and we’ve had some really nice feedback, particularly from some of our regular guests, who were enjoying the new facilities.”
When Serco unveiled its new trains earlier this month, it said passengers would experience an overnight stay in “a hotel on wheels”.
The 75 new carriages offer en-suite double rooms for the first time.
There are 484 rooms available, initially on the Lowlander route between London and Glasgow/Edinburgh.
They will be followed by a Highlander route between London and Aberdeen, Inverness and Fort William.
The trains have been part-funded by capital grants from both the Scottish and UK governments.
Mr Flaherty added: “We always knew there would be some niggles that would come up as we put the trains into service and we’ve dealt with those overnight.
“For the vast majority of people last night, it was a good experience.”