There are delays of up to 30 minutes on First Transpennine Express services between Edinburgh Waverley and Carlisle due to flooding between Lockerbie and Carlisle.
Trains have resumed between Lockerbie and Carlisle, but delays are expected until around 3pm.
There are also delays on Virgin Trains between Glasgow Central and Carlisle, and between Edinburgh Waverley and Carlisle due to flooding.
Tickets are being accepted on East Coast, ScotRail and Northern Rail services.
More top news
Colder, windier and wetter weather is on the way.
Will the 'potentially historic' snow storm hitting the US, find its way to the UK?
ComRes polling agency chairman says the next 100 days will be be gruelling in the most uncertain General Election that anyone can remember.