Oggy would be the happiest of cats if three cockroaches hadn't decided to settle inside his comfortable home.
Under prohibition, Dee Dee is appointed by Joey and Marky to fetch a tin. Dee Dee decides to compete with Al Capone. Oggy is quick to unmask Dee Dee and put an end to his traffic that starves the city.
Jack, American adventurer of the early 20th century, brings back from the expedition a gorilla to mount a show on Broadway. Joey wants to seize the primate to make a fortune. Enervated by cockroaches, King Kong fled by taking Olivia away.
Oggy's Viking Village asks Thor, the Lord of Thunder, to protect the village from monsters. Since Thor is very powerful, it is easy for him to get rid of the monsters. However, the great Thor is afraid of cockroaches, and it is up to Oggy to save the day!
Oggy Maggon has made friends with the Stone Age’s first invention, the Wheel.
Jack decides to help Oggy by showing him his inventions, purely designed for cockroach removal - which is, in fact, overcomplex and technologically advanced versions of the flyswatter.
Oggy returns home after a night out with Jack and only wants to go to sleep but the cockroaches have other ideas.
In this fairytale-like story, Oggy accidentally runs over a frog whilst returning home from his shopping. He then tries to kiss it better, only to learn that this frog is actually a fairy, who decides to make a van out of his shopping bag. When Jack learns of Oggy's situation, he decides to find another frog/fairy in order to have a big night out.
Jack bought Oggy a remote control car and they want to race with them, but then the cars are now annoyances and chasing – and chased by the cockroaches to run them all over.
Oggy's granny comes to visit. It is her birthday, and what she wants is three dead cockroaches.
Three alien cockroaches from another planet (obviously genetically resembling Dee Dee, Marky and Joey) visit Oggy's household. They constantly shape-shift Oggy and Jack into different objects and share good moments with the regular cockroaches.
Taking a simple bath soon escalates into a desperate struggle for Oggy when the cockroaches deflates his floating ring, especially when Oggy is extremely afraid of water.
Another series of cockroach pranks results in Oggy falling into a photocopier, and trapped inside a piece of paper. Can Oggy find a way out of this situation?
After watching a game of soccer on TV, cockroach Joey introduces it to Dee Dee and Marky, and decide to have their own game. However, they soon learn that finding the perfect pitch is no walk in the park.
It is all out Cyberspace War as Oggy, with his vacuum cleaner, and Joey takes the daring voyage in the electrical system to the internet in order to return to the real world – however, system errors, bugs, power flows and even Jack himself are hellbent on slowing Oggy and Joey down.
The cockroaches play a hit-and-run prank where they frame Oggy by dressing up as him and attacking Jack.
Oggy was just minding his business, gardening the grass while the cockroaches made it worse by making them bigger. Not only the garden got bigger, but also the animals like the hedgehog and the angry bunny.
One night a green giant comes to Oggy's neighborhood and Joey meets with him. He gives Joey a can of magic beans, which make Joey grow taller when he eats them. Joey spends all night trying to grow up enough to scare Oggy. But no matter how huge he grows, whenever he confronts Oggy, he is still shorter.
Oggy's cruise trip is rudely interrupted by cockroach Dee Dee while Jack, Marky and Joey are feeling... seasick.
Oggy and Jack share a ride in a remote-controlled hot-air balloon. However, it soon becomes a joyride when their remote ends up in the cockroaches' hands.
Oggy is going to the beach for what he thinks will be a relaxing day off. What he does not notice, is that the cockroaches has decided to tag along. And when Oggy and the cockroaches are near each other, trouble is bound to happen.
Oggy found a poor snail and kept it as a pet and bought a lot of snails he enjoy. However, he is about to be in for one slippery ride.
Jack and Oggy are having a racing contest in order to decide who should be allowed to use the TV's remote-control – something that only results in more mayhem.
Oggy finds a book on flower power and decides to become a peaceful hippy. The cockroaches try to provoke him into losing his temper.
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