The show centers on Oggy, a content and lazy, albeit very tender fat blue cat, who would usually spend his days watching TV and cooking - if it wasn't for the three pesky roaches in the household: Joey, Dee Dee and Marky (named after members of the punk group Ramones). The trio seems to enjoy generally making Oggy's life miserable, which involves mischief ranging from (in most cases) plundering his fridge to such awkward things like hijacking the train Oggy just boarded.
Ever since the world was born, two forces have been locked in perpetual battle. Their struggle is so Manichean, so ferocious, so Herculean that it makes the clash between good and evil look like a game of checkers! This ancestral duel is so ancient and so merciless that it can only be, Oggy against the Cockroaches!