ScotRail cancelled all trains to North Berwick and Dunbar, while Virgin Trains East Coast and CrossCountry services were delayed.
The disruption was caused by a ballast-cleaning train breaking down at 2:50am near Drem in East Lothian.
Network Rail said there were difficulties moving the half-mile long train because it lost power while cleaning ballast under the track.
It blocked one track while the other was used by trains in each direction.
Disruption continued until about 2pm - 11 hours after the incident happened.
ScotRail trains only ran on the line between Edinburgh and Prestonpans, with replacement buses to and from North Berwick.
BACKGROUND: Fault-detecting Flying Banana train caused delaysThe ScotRail Alliance, which includes Network Rail said: "Unfortunately, an engineering train has broken down in the Drem area and we're unable to run a full service between Edinburgh and North Berwick/Dunbar.
"Staff are still on site working on the train, but we don't have an estimate for when we might get the train moved.
"Train services between Edinburgh and Dunbar will be suspended.
"Services between Edinburgh and North Berwick will run between Edinburgh and Prestonpans only."
National Rail Enquiries stated: "Trains will therefore need to travel in both directions using only one of the two tracks, meaning fewer trains will be able to run.
"Train services may be cancelled, revised or delayed by up to 30 minutes.
"Disruption is expected to continue until at least 13.30."
A ScotRail spokesperson said: “We apologise for the disruption to customer journeys today due to these over-running engineering works."
"We remind customers that they can make a claim under our Delay Repay Guarantee if delayed by 30 minutes or more."