The two felines, one black and the other a white tabby, were found behind the Highwoods Tesco store.
A member of the public found the cats and called immediately the RSPCA on Sunday, January 10.
RSPCA inspector Adam Jones, who is now investigating, states: “Both cats were very frightened and were in poor condition when they came in to us.
“I’d like to find out how they came to be dumped in this condition and at this location.”
The pair of cats, now named Black and Magic, were taken to the charity’s North East Essex branch, in Colchester before they were transferred on to an animal care centre in Kent.
They are receiving treatment for skin lesions but are doing fairly well, according to centre bosses.
Anyone with any information about these two particular cats or what happened to them should call the RSPCA’s appeal line on 0300 123 8018.