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Alarm was raised after a member of the public found the deceased animals at around 7.25pm in the communal garden of a property on Harewood Crescent.
The puppies, which are believed to be Staffordshire bull terriers, were discovered wrapped in toilet paper and buried in a shallow hole in the communal garden.
A post mortem examination found that the dogs had not fed or passed their first faeces suggesting they were either stillborn or died shortly after birth.
Scottish SPCA inspector John Toule said it is vital that the charity contacts the owner of these dogs to make sure the mother and any other puppies are safe and healthy.
Mr Toule said: “This was a very distressing incident for the person who found these puppies.
“The dogs were wrapped in toilet paper and buried in a shallow hole in the communal garden of the property.
“They appeared to have been recently placed in the garden and were probably buried the same day as they were found.
“The puppies are a small to medium type of dog and we believe them to be Staffordshire bull terriers or a similar breed.
“We’d like to find the owner of these dogs as we have concerns for any remaining pups and their mother and would like to make sure they are all healthy and receiving any veterinary care they may need.”
Contact the SPCA’s confidential animal helpline on 03000 999 999 with information.