The rail operator's official twitter account has been sharing tweets to highlight the problem and to urge all of their passengers to abide by the law.
Face coverings are mandatory in Scotland in enclosed spaces where physical distancing is made more difficult, including on public transport and in shops.
However there are exemptions for people with breathing difficulties, medical conditions and children under the age of five. Drivers or checkout assistants who are physically separated from passengers or customers by screens, for instance, are also exempt.
And certain situations such as eating or drinking or taking medication allow for the removal of face coverings.
In a tweet yesterday, ScotRail said: "We've noticed some folk have started removing their face coverings on the train once staff are out of sight. Please, please don't do this.
"It's vital that everyone who can, covers their face to protect those around them."
One tweeter responded to say: "Someone sitting in same carriage as me didn't have one on. Another guy pulled mask down to his neck till he saw the guard walk through and even when he did pull it up, he didn't cover his nose."
And one hospital worker responded to say they'd seen groups of teenagers not wearing face coverings on board between Hyndland and Partick during recent weekends, a situation which ScotRail says they are monitoring through CCTV.
In a further tweet today, ScotRail said: "Can anyone currently travelling on our trains, with their face covering not placed fully over their mouth and nose, position it correctly and leave it there for the full journey.*
This is vital to keep other customers and our staff safe."
They also referred to a list of exemptions HERE and shared a picture of a staff member wearing a face mask correctly.
A ScotRail spokesperson said: “While it’s encouraging to see that most people across the country are following the requirement and covering their face for their full journey, we need everyone to take personal responsibility for their travel choices.
“The mandatory wearing of face coverings helps keep you, your fellow customers, and our people safe.”
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