Nineteen 100-year-old trees in a churchyard could be felled to protect public safety.
The horse chestnut trees in Holy Trinity churchyard in Barnstaple have been declining rapidly, with two already dead.
The maintenance of the churchyard has fallen to North Devon Council after it was formally closed earlier this year.
This includes grass cutting, maintaining walls and looking after the trees that line the churchyard's footpath.
The issue of the horse chestnuts was raised at the council's last meeting of the executive.
A report was presented which outlined two options available.
The first would be to fell all 19 trees at a cost of £10,640 and replace them in other positions throughout the churchyard. They could not be replanted in the same position.
The second option is to fell the two dead trees and pollard the other 17 in order to monitor their growth. The horse chestnuts in the churchyard were pollarded in 1997, which the report states is the reason for their decline in health.
The report presented to the executive recommended the council proceed with the first option.
Diana Hill, head of property and technical services, said: "The horse chestnuts' life has expired. The church has removed some that are past their life expectancy. We have been considering other options.
"They are a wonderful site but the gravestones are too squashed together and we cannot replace like for like which is what we would want to do."
"It looks OK but the reality is the experts have said these trees are dying."
She said that option one would cost the council less in the long term as the remaining trees will all need to be felled at some point in the future.
North Devon councillor Faye Webber said that the public would not be happy with a decision to remove the trees from the churchyard. She said:"I do not want to see these trees go. They add greenery to the town. We think there is going to be a bit of an uproar."
Fellow district councillor Mike Edmunds said: "If we didn't do anything and one of these trees fell on a gravestone we would have a much bigger problem."
It was agreed by the executive to hold a site meeting at the churchyard on January 4 to discuss the best option with regard to the trees.