Just like other breeds of dogs, greyhounds can be interested in chasing cats – however, greyhounds are so much faster that they stand a far greater chance of catching them! Some greyhounds can settle with small dogs and cats and it is one of the most important issues to deal with when you first adopt a dog. Always be aware that although your greyhound may be completely safe with his own family cat – off territory he may view anything that runs as fair game – so be prepared!