The 05.38 service from Cathedral to Parkgate and the 06:39 service from Parkgate to Cathedral were the first to be cancelled.
The 07:09 from Parkgate was also cancelled and Stagecoach Supertram has announced that the 07:40 from Cathedral to Parkgate and the 08:09 from Parkgate to Cathedral will also not run.
The tram train service was launched last October to improve links between Rotherham and Sheffield.
The project cost £75 million.
More to follow.