A study says if conditions are right, then there is no reason not to have both types of animal under the same roof.
But the cat has to feel comfortable that it is the “main controller” in the relationship.
Dogs will not mind so long as it is clear who is boss because they are more easygoing about cohabiting with a different species.
Only around seven per cent of UK households are thought to own both a cat and a dog. There is still a feeling among many who have one or the other that the two species do not get on.
That is wrong, say researchers from the University of Lincoln’s School of Life Sciences, who asked 1,131 pet owners details of their animals’ behaviour.
They found cats are far more fussy than dogs over who they share their home with but behaviour changes when the pets are comfortable with each other because the cat is… top dog.
Behaviour includes one animal rolling over in front of the other, sharing food or a bed and picking up toys to take to the other, the Journal of Veterinary Behaviour reports.
And there are certain ways to both make the relationship work and to tell it is successful, said study authors Jessica Thomson, Sophie Hall and Daniel Mills.
The age of the cat, rather than that of the dog, is an important factor.
The younger the cat the better the relationship tends to be over the years, they found.
Where there is any animosity, it is more likely to feature the cat being aggressive to the dog rather than the other way round. But actual injury despite threats to scratch is very rare.
The online survey involved homes in Britain, the US, Canada and Australia.
Of those with both types of pet, 83 per cent reported that the cat was comfortable with the canine and 92 per cent said the dog was comfortable living with a feline.
Cats are more likely to roll over in front of the dog than the other way round but dogs are more likely to be happy to share their food or bed.
The report said: “Although cats and dogs were rarely perceived as being uncomfortable together, cats were perceived to be more frequently uncomfortable with dogs than vice versa.”
Evolutionary reasons behind the results could be down to dogs being domesticated a lot earlier than cats.
This leads to them being, as a species, better behaved and more controllable than cats.
Dogs, being bigger, could feel more comfortable with a smaller animal around them than the other way round.
And though they can get along, the survey found that: “Very few owners scored their cat-dog relationship a nine or 10, indicating that although the relationship could largely be considered amicable, it was rarely close.”