The charges were that they caused unnecessary suffering to 35 cats at a property on Barkerend Road, and that they did not take steps to ensure the needs of 35 cats were met.
Both will be sentenced next month.
Andrew Davidson, prosecuting on behalf of the RSPCA, said: “There were 35 cats that lived at the property. All were neglected to various degrees.
“There was a failure to provide adequate nutrition or infection control.”
The RSPCA had attended after emergency services had raised concerns about the cats after being called to the house on a separate incident.
Mr Davidson said: “There was a large amount of faeces throughout the house, as well as a smell of ammonia.
“There was the smell of faeces everywhere.
“Some of the cats were extremely thin, and were suffering from hair loss.
“There were very poor conditions in the property.”
The court heard that two of the cats belonged to Mr Dunn and 33 belonged to Mrs Dunn.
There was no suggestion that the pair had deliberately mistreated the cats, but that the sheer number of animals had caused the issues.
No cats had to be put down, and after being treated the cats returned to a healthy weight.
The pair will be sentenced on June 29.