A girl gets a dinosaur that only knows one word, and somehow that becomes the entire show. The premise is deliberately dumb in the way that 90s adventure comedies understood: commit completely to the bit, pack every episode with invention and chaos, let the character relationships carry you through the absurdity. Muka-Muka doesn't apologize for being exactly what it is, a 51-episode ride on pure earnest weirdness, where a time machine and a babbling dinosaur are treated as normal problems to solve.
Uiba Shikatani, whose father runs a pet shop, is crushed when a batch of reptile eggs never hatches. Hoping to lift her spirits, her father brings home a big striped egg, and out comes a green baby dinosaur. He takes Uiba for his mother, and she names him Muka-Muka, since those are the only words he can say. Muka-Muka eats and plays constantly, stirring up plenty of trouble in the local shopping district, where Uiba's childhood friend Senta, her older friend Hazuki and the other neighbors live. The little dinosaur soon becomes the talk of the town and catches the eye of the town's professor, a maker of odd inventions. One of them is a time machine that sends the Shikatanis, along with other families and their houses, back to prehistoric times, where they meet more dinosaurs and magical beings. The result is a comedy adventure.