When Do Domestic Rabbits Sleep? At BackyardBunnyNews, we help people who want to raise rabbits and bunnies by collating information about the hare-raising experience. Most rabbits sleep when they aren’t awake. Most rabbits are most active at dawn and dusk, which is why most people assume that they are nocturnal creatures. However, they are actually crepuscular animals. The modern European rabbit is thought to have originated in the Mediterranean around 43 AD. It was first brought over by the Romans as a food source but has since become a popular pet in Britain and other parts of the world. Rabbits are prolific; they can have up to 12 babies in one litter.