Trains are now running normally after the flooding at Pontyclun.
Trains are now running normally between Holyhead and Bangor after earlier delays because of a signalling problem at Ty Croes.
The Welsh Secretary, David Jones, has expressed his pleasure at today's Network Rail announcement.
Mr Jones described a modern rail network in Wales as "crucial" for the growth of the country's economy.
He also welcomed news that the mainline between London and Cardiff will be electrified by 2018.
The Arriva Trains service between Llanrwst and Blaenau Ffestiniog has been suspended due to flooding.The company says it is currently looking to source replacement road transport but has no current estimate for when a normal service will resume.
Replacement bus service running on Arriva Trains Wales between Machynlleth and Caersws due to flooding.
Simon Calder, a travel journalist, says the disruption at London Paddington train station could continue into the weekend.
A number of services, including trains to and from south Wales, were cancelled after signalling problems caused major disruption to a line.
There is disruption on Arriva Trains Wales between Abercynon South and Merthyr Tydfil due to flooding at Merthyr Vale.
The company says all lines are currently blocked and it does not have an estimate for when a normal service will resume.
There are delays of up to 45 minutes because of signalling problems between Cardiff Central and Newport until further notice
Network Rail and Arriva Trains Wales Directors have confirmed that services will return to the normal timetable tomorrow.
Following a landslip between Cardiff Central and Queen St station on the 9th August, Arriva Trains Wales have been operating an Emergency Timetable.
This has been whilst Network Rail carry out repair work to the track between the stations.
There are safety checks being made near Severn Tunnel Junction.
Because of this, there are delays of up to 30 minutes between Newport and Bristol / Gloucester. These delays will continue until further notice.