Services between Brighton and Southampton/Portsmouth are impacted.
A Southern spokesperson said: "We have been informed of a power 'tripping' in the Fishbourne area which means trains are currently unable to run between Barnham and Havant.
"The power supply to trains 'tripped out' which means that power cannot be restored until the cause of the power trippings has been identified. Trains have been inspected and engineers are currently walking the track to see if the problem is track related.
"If you are on a stationary train, please remain on board unless you are instructed otherwise. We are working to get you into stations as soon as possible.
"Staff are on site and in the process of starting to evacuate trains that are not in stations. Please listen to the instructions of the driver, on board supervisor and track workers."
West Sussex Fire and Rescue Service has been called to an incident in Salthill Road, Fishbourne this morning which is believed to be related.
Southern added: "The majority of trains between Angmering and Hove are running as planned. There are a few cancellations due to the incident so if you are travelling between these stations, please check journey planners before you travel."
Rail tickets will be accepted on Stagecoach buses including the 700 between Brighton, Littlehampton, Havant and Portsmouth and the 56 between Bosham and Chichester.
Updates to follow.