UNION representatives are expected to meet Royal Mail staff on Monday to discuss concerns over a new cost-cutting system.
Postmen and women in Darlington say that since the Royal Mail combined its first and second posts, workers have been going off sick with stress.
They also say that deliveries in the town have been late and that thousands of letters went undelivered yesterday.
The new system was intended to make postal services more efficient, but staff say that it has instead led to long delays and complaints from businesses and residents.
Now postmen and women in the town say they are having to work longer hours to get all the post out and, at the same time, are being confronted by residents furious that their post is up to six hours late.
In Darlington, some mail is not arriving until 3pm.
One worker, who did not want to be named, said: "Morale in the office is really bad. Managers and all the staff are so stressed that some are leaving, others are going off sick with stress, and people are actually breaking down and crying.
"The walks we do are only supposed to take three and a half hours but they are taking six hours under the new system."
A spokeswoman for the Royal Mail was unable to confirm whether letters had been undelivered last night, but said: "The introduction of single daily delivery is a major change for every office across the country.
"It is being implemented following months of careful planning and with such a major change as this there are almost inevitably going to be teething problems.
"However we are determined to iron these out."
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