A bid to list buildings at the decommissioned Trawsfynydd nuclear power station in Gwynedd has been refused by Wales' Heritage Minister Alun Ffred Jones.
Campaigners wanted the structures saved as they were designed by Sir Basil Spence, the architect behind Coventry Cathedral.
The power station was the first inland nuclear power station in Britain.
The towers' height is set to be reduced by half at the end of this year.
The building was constructed between 1959 and 1963 to a design by Sir Basil Spence, with garden designer Dame Sylvia Crowe as landscape consultant.
It began generating electricity in January 1965 as Britain's fourth nuclear power station.
The power station was taken off line in 1991 and decommissioning began in 1993.
The minister Alun Ffred Jones was asked to consider whether the reactor towers met the criteria for listing 20th century buildings.
His decision not to list them clears the way for the towers to be partially torn down, with work expected to start towards the end of this year.
Clayton Hirst, who campaigned to save the towers, said he was "obviously disappointed at the decision, but satisfied Cadw looked at it in a thorough and vigorous process".
Writing about his reasons for saving the towers on the Waleshome.org website Mr Hirst said Trawsfynydd should sit alongside Coventry Cathedral as one of Spence's greatest works.
"The problem is that it is tainted by what is contained within," he wrote.
"Not only is the site contaminated with radioactive material, but the very fact that it houses two worn out nuclear reactors contaminates the public's attitude towards the structure, making it one of Wales' most unloved buildings."
The Twentieth Century society, which campaigns for the preservation for Britain's modern architectural heritage was asked to back the campaign for the listing, but declined to do so because there were too many "issues".
Although they agree the building is worth saving "architecturally" there were too many other considerations, not least the fact that the building is full of "toxic material", according to the society's Jon Wright.
"It's an important building, but it doesn't surprise me that it's not been granted listed status," said Mr Wright.
He added the society believed it was far better to keep it there than cover it up, which will happen under the decommissioning plans.
"You can't pretend it was never there, that's a bit silly," he said.
"Better to leave it as it is until it is decided how to deal with what's inside."
The station was built with all local mortar and stone, and it was designed for the landscape, he added.
"Even the lake is man-made, so it's not as natural a place as it looks," Mr Wright said.
"I am sorry it hasn't been listed, but pleased Cadw looked at it closely," he added.