Both incidents happened in the central Scotland area on Saturday evening.
In the first incident, two men racially abused a man and another couple at around 8.20pm on the 19.44 Glasgow Queen Street to Dunblane service.
Two unconnected hate crimes on board trains are being investigated by transport police.
Both incidents happened in the central Scotland area on Saturday evening.
In the first incident, two men racially abused a man and another couple at around 8.20pm on the 19.44 Glasgow Queen Street to Dunblane service.
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