The lines between Glasgow Queen Street and Croy and Kilmarnock and Ayr are currently closed as emergency services attend the tragic incidents.
The Glasgow Queen Street and Croy incident was announced at around 8pm and the Kilmarnock and Ayr incident at 7.40pm on Thursday by ScotRail.
ScotRail is currently diverting trains via Cumbernauld.
There are unaffected direct services between Edinburgh and Glasgow Central via Shotts, as well as between Edinburgh and Glasgow Queen Street via Bathgate.
A ScotRail spokesperson said: “I'm afraid that a person has also been struck by a train between Croy and Glasgow Queen Street.
"The line in the area is closed while the emergency services attend.
"Sadly, a person has been struck by a train between Kilmarnock and Ayr.
"The emergency services are on their way.
"We can't run trains on this route for now, but services between Glasgow Central and Ayr aren't affected.”