Uiba Shikatani, the daughter of a pet shop owner, is heartbroken after some reptile eggs fail to hatch. In his attempts to cheer her up, her father brings home a large, striped egg, which he hopes will successfully hatch (unexpectedly into a green dinosaur whom they call "Muka-Muka," which are the only words which the baby reptile can speak).

Muka-Muka soon becomes the talk of the town and comes into the interest of the town's professor and his wacky inventions, including a time machine which successfully teleports the Shikatani's among other families and their homes to pre-historic times where they encounter several other dinosaurs and enchanted beings on their adventures.