Northern Rail are reporting that all services running between the two stations will be either cancelled or delayed following damage to the overhead electric cables.
Customers wishing to travel to stations between Doncaster and Leeds are being advised to instead travel on Leeds - Sheffield services via Moorthorpe.
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These services will call at Fitzwilliam, Sandal and Agbrigg, Wakefield Westgate and Outwood.
Alternatively customers can also travel on Sheffield - Adwick services, calling at Bentley and Adwick.
Rail replacement transport is now in operation between Wakefield Westgate and Doncaster with passengers warned that road replacements will add around 45 minutes to journey times.
Northern passengers will also be to use their tickets on Cross Country services between Sheffield and Leeds.
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