Rabbits, guinea pigs, rats, mice, ferrets, chinchillas, hamsters are often seen as an easy, first pet for children.
However, the animal charity said small does not necessarily mean simple as they can have complex needs.
Dr Jane Tyson, the RSPCA’s rabbit and rodent welfare expert: “Many people think the RSPCA only rescues and rehomes cats and dogs but this is not the case.
"We see thousands of small furries coming into our care every year and often this is as a result of owners being unable to cope with caring for these animals who they thought would be easy to look after.”
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This Adoptober the RSPCA is shining a light on rabbits and small furries in its care which are looking for homes.
Last year the animal charity rehomed 2,752 rabbits.
Jane added: “Small furries can make great pets but they are often very misunderstood. One of the biggest issues we see with small pets such as these is people taking them on with little or no research, often buying them on impulse because their children have asked for them.
"This can lead to families struggling to cope once they realise the large amount of time, money and care these animals actually need."