A broken down train has closed the line between Ore and Ashford International today (Tuesday, November 5).
Southern said services running through these stations may be cancelled, delayed or terminated at and started back from Rye.
Appledore Kent, Ham Street and Ashford International will not be served, it said.
Southern said there will be no Southern services from Appledore, Ham Street or Ashford International until further notice.
A shuttle train service will operate between Eastbourne, Hastings and Rye, but this may not be able to run as frequently as the normal train service, the company said.
The firm said the problems started earlier today due to an engineering train breaking down in the Ham Street area.
Network Rail is working with the operator of the engineering train to get it moving as quickly as possible, Southern said.
But it said there are reports that the train may have been causing issues with the signalling system as well, so the problems may take some time to be resolved.