They appear as villainous invaders on the original TMNT show in the episode "Night of the Dark Turtle" (where Donatello becomes a Batman-like superhero) under the command of a Captain Zorax; but there they do not call themselves the "Triceraton Republic", instead their government is called the "Triceraton Empire". In this series, they are able to breath oxygen the same way Earth creatures do. The Triceratons invaded Earth, claiming it as part of their empire and planned to send it through their Star Gate to their homeworlds to strip it clean.
Leonardo, Raphael, and Michelangelo fought them only to be defeated since they didn’t have Donatello. However their plan was thwarted, when Donatello was able to convince the Triceratons that he was ruler of the Earth and the animatronic dinosaurs from the Natural History Museum were his minions. He also used Shredder’s powerful Micro Blaster to convince the Triceratons that he and his brothers were far superior to the Triceratons powers and abilities causing them to leave Earth.