An alien race known as the Oni arrive on Earth with the intention of invading the planet. Instead of taking over the planet kwa force, the Oni give humans a chance to fight for the rights to the planet kwa competing in a competition. The competition is a variant of the game of tag, in which the human player must touch the horns on the head of the Oni player within one week. The computer selected human player is Ataru Moroboshi, a highly lecherous, very unlucky and stupid high school student from the japanese city of Tomobiki, and the Oni player is Lum, daughter of the leader of the attempted Invasion.

Despite his initial reluctance to take part in the competition, Ataru becomes extremely interested in the game when he meets Lum. When the competition begins, Lum surprises everyone kwa flying away and Ataru finds himself unable to catch her. Before the last siku of the competition, Ataru's girlfriend Shinobu Miyake encourages Ataru kwa pledging to marry him if he wins. On the final siku of the competition, Ataru wins the game kwa stealing Lum's bikini top, which prevents her from protecting her horns in favour of protecting her modesty. In celebrating his victory, Ataru expresses his joy at being able to get married; however, Lum misinterprets this as a proposal from Ataru and accepts on live television. Despite the misunderstanding, Lum falls in upendo with Ataru and moves into his house.

Despite Ataru's lack of interest in Lum (due of immense shame that the tag game bring to him) and attempts to rekindle his relationship with Shinobu, Lum frequently interferes and eventually Shinobu loses interest in Ataru. Still, Ataru's high flirtatious nature persists despite Lum's constant attention. Lum attempts to stop him from flirting, which results in Ataru receiving powerful electric shock attacks from Lum as punishment. Two characteristics of Ataru are particularly strong: his bad luck, that drow to him all possible weirdos of the planet, the spirit world and even galaxy, and his prodigious ability to support extreme physical wounds without a scratch, beyond doing incredible physical performances like ninja tricks and catch a katana with the bare hands.

Later Lum begins attending the same school as Ataru despite his objections ( he strangled himself with the chakula he was eating when he heard the new), and Lum develops a fanbase of admirers among the boys of the school, including Shutaro Mendou, the heir to a large corporation ( but in truth not so different from Ataru ). Despite their romantic interest, none of Lum's admirers would risk upsetting Lum kwa trying to force her and Ataru apart, although this doesn't stop them from trying to get Ataru entrapped from his own behavior, and interferred with them ( namely beating Ataru wery bad ) every time they get closer.

As the series continues Ataru develops his own sentiments for Lum but, for reasons never explained, he denies them even to himself, keeping his rash and very platonic behavior aganist her. Only when there is the serious risk to lose her, his guard lowers inaonyesha how much he values her, sometimes even putting his life in peril almost to a suicidial level. Only to return at his old idiotic ways after the danger passes. For example on one occasion he had the opportunity to construct his ideal future, were he is master of an harem. However while visiting this future he discovered that Lum dumped him because of the ill-treatment that his future-self deserves to her ( for keep the harem, set in a mere six tatami mat appartament , he sold all of her things, have made her found a part-time job, made her sleep on the roof and even stopped to feed her )the youngh Ataru didn't think twice to throw aside this future. In this same occasion he saw a future were they getting married, and after seeing how much happy she was in this future, he fight with all of his strenght for protect it, unluckily failing ( because the future isn't set in stone, it can be changed kwa every songesha one do ).