After the spectacular defeat of a fresh centurion, Caesar sends the patrician Lucullus to capture Getafix and throw him off the edge of the world (as the world is considered to be flat at that time in our history, and Rome at the center of it). Caesar knew that the magic potion brewed by Getafix was the secret to Gauls superhuman strength. Getting rid of Getafix would remove the supply of potion and make it easy for Caesar to capture Gaul. Getafix cannot be killed as druids are immortal, so Caesar believes that once thrown off the edge of the world, Getafix would roam around in wilderness forever.In Gaul, Unhygienix lacks fresh fish (as always), which starts a fight, spilling Getafix's magic potion. To brew a fresh batch of the magic potion & because fresh fish is a vital ingredient thereof, Asterix and Obelix go fishing while Getafix gathers herbs, accompanied by Dogmatix.In the forest, Getafix and Dogmatix are captured by Lucullus, who disguises himself as a druid to lure Getafix. Aboard a Roman galley bound for the "world's edge", they pass Asterix and Obelix, who pursue them, using Obelix as an outboard motor until he is diverted by the aroma of food from a passing pirate ship, and then blown off course by a violent storm. After a long pursuit, a dolphin brings Dogmatix (whom Lucullus had dropped overboard) and guides them to the Romans. Seeing the Gauls and mistaking the North American coast for the world's edge, the Romans launch Getafix from a catapult, then return to Rome, while Asterix and Obelix make landfall. In Gaul, Caesar lays siege to their village and waits for the last of the magic potion to run out.Asterix and Obelix explore the new land looking for Getafix and live off the indigenous turkeys. Asterix is captured while Obelix hunts for breakfast, but instead catches a Native American whom he mistakes for a disguised Roman. When he finds Asterix gone and his helmet lying on the ground, he has Dogmatix follow the scent. On the way he saves a Native American chief's daughter from a stampede of bison. In the Native American village, Asterix is tied with Getafix to a pole, menaced by the natives. Obelix and the girl arrive to save them, and the chief frees them hearing about Obelix's feats from his daughter; thus, enraging the medicine man. The medicine man is insulted again when Getafix proves himself the superior magician. That night, the medicine man pretends to offer peace, but uses the peace pipe to drug the visitors.In the morning Obelix is suffering hallucinations of the drugs and Getafix has been taken prisoner by the medicine man, who demands the recipe of the magic potion. When Getafix refuses, the medicine man releases a grizzly bear against him. Asterix wake up in his tent and is guided to the cave by Dogmatix. He arrives to defeat the bear and its keeper. Minihooha, the chief's daughter, cures Obelix with a huge meal. The natives give them a canoe which Obelix paddles tirelessly across the ocean.At their village, Cacofonix reveals that Caesar has captured the villagers, whereupon Asterix and Obelix - disguised as legionaries - take gourds of fresh potion to their friends imprisoned at the nearby camp of Compendium. Thus enabled, the Gauls free themselves, destroy the camp, and return victorious to their village. During the battle, Caesar escapes disguised as a wine barrel, while Lucullus is consumed alive by Caesar's pet panther.