ScotRail is warning customers to check their journeys before they travel on Monday, in case of further disruption.
The advice comes after cancellations affected many services on Sunday. Some routes ran less frequently or finished earlier than usual.
The operator said the disruption was due to fewer than normal train drivers taking on overtime as a pay dispute continues.
About a quarter of services are believed to have been cancelled.
The BBC said the train drivers' union Aslef informed ScotRail on Friday it was considering a ballot for industrial action in the pay dispute.
In the meantime, a number of train drivers have refused to work extra Sunday shifts and overtime, which has had an impact on services.
ScotRail said it was traditional in the rail industry for Sunday services to rely on drivers taking on extra shifts as overtime.
There is now concern from ScotRail that shifts which have to be covered at short notice during the week, due to illness for example, will also be difficult to fill.