As cat always sleep, do you ever winder if they have dream? Cats sleep roughly 16-18 hours a day. Like humans, they experience Rapid Eye Movement (REM) Sleep. The REM stage is when most dreaming occurs. This happens when they are relaxed enough to enter a deep sleep. So we know now that cats do dream, but what do cats dream about when they sleep? Just like humans, the dream of cats are often based on realistic experiences. Also, they may have sweet dreams and nightmares just like we do.