The plant has had serious problems in the past
Critics of the Wylfa Nuclear power station on Anglesey say the latest shutdown of the plant is proof it should close for good.
On Friday, the plant's owner, British Nuclear Fuels, confirmed that both reactors have been temporarily shut, after problems were uncovered during a routine maintenance check.
BBC Wales was told that a reactor was closed down after problems were detected during a routine maintenance check, which has to take place every two years.
Both reactors were closed down as a precaution.
Owners British Nuclear Fuels Limited have not said how long the plant is likely to remain closed, but it is believed it could be several weeks.
Tim Jones, head of media for BNFL Magnox, said the routine overhaul on reactor number one started a few weeks ago.
The latest problem is yet another blow to the future of the power station, which was opened in 1971 and employs 500 people. Generation of electricity is scheduled to cease in 2010.
The station re-opened two years ago, after safety concerns forced a 15-month shutdown which cost BNFL an estimated £200m.
The lastest difficulties are said to be unrelated to the technical problems suffered in 2001.
A statement from BNFL released on Friday said : "Reactor one has been shut down for its statutory overhaul. Each reactor is shut down every two years and inspections are carried out of components inside and outside the reactor pressure vessel.
"Inspections inside the reactor vessel showed there were a few defects present in a small number of welds associated with brackets which support the boiler tubes in the reactor.
"A safety case had been made for return to service. During the preparation of the case, it was identified that further information is required about the condition of the supports.
"Because similar information is required on reactor two, in line with the station's safety culture and its conservative approach on any matters associated with reactor safety, the conservative decision was taken to shut down reactor two to obtain that information."
BNFL is in the process of preparing a case to bid for an extension to the plant's licence next year.
But critics have insisted the latest problems demonstrate that the station should now close.
Neil Crumpton, energy spokesperson for Friends of the Earth Cymru said:" We call yet again for the closure of the Wylfa nuclear power station on safety grounds.
"But there is a wider point here also. Nuclear power is seriously unreliable and unpredictable especially if a problem affects a whole series of similar reactors."
Dylan Morgan from the pressure group People Against Wylfa B (PAWB) said the latest setback should prompt action.
"Politicians at all levels must now realise that the intense problems associated with Wylfa relating to the station's age make it virtually impossible for BNFL to make a case for extending the station's life from 2004 to 2010," he said.
" The last time faulty welds were found in Wylfa in April 2000, the station closed for 16 months - how long this time?
"The faulty welds then were outside the pressure chamber. The faulty welds found this week are inside the pressure chamber, and access to them is far more difficult with a much higher risk of an overdose of radiation.
"How much more taxpayers' money is the government prepared to pour into this bottomless pit?"