The Oni, a mysterious race of aliens resembling mythological Japanese demons, come to Earth intending simply to invade and take over. Represented by their leader Invader, he tells the people of Earth that they have but one chanceIf Ataru Moroboshi, a teenage boy chosen randomly by a computer as Earth's champion, can defeat Invader's daughter Lum in a game of tag (by touching the horns on her head), the Oni will just pack up and leave quietly.
Ataru, who has glandular drives undreamed of by even the most lascivious of high school boys, is only too eager to get his hands on the delectable Lum. This proves nearly impossible when he discovers she has the power to fly. Day after day, Ataru makes numerous attempts to touch her horns but he fails spectacularly day after day. The final day was approaching, and Earth's fate hung in the balance. A balance which depended on the efforts of one hopeless loser.
The night before the final day Ataru's tentative girlfriend Shinobu promises him in desperation that if he can win, she'll marry him. With this on his mind Ataru finally becomes serious about winning. Using dirty trickery, he steals Lum's bikini top and then grabs her horns as she tries to retrieve it. A dirty way to win, but it's a victory nonetheless. The Earth is saved thanks to Ataru. Now the Oni will leave and never again plague the people of Earth.
Or so it seemed. For right at the moment of triumph Ataru proclaims "now I can get married!" Lum misinterprets this as a marriage proposal to her and eagerly accepts to become Ataru's wife.
After publically undergoing so much pain and humiliation, and because she continually hinders his "girl-hunts", Ataru seems to have lost interest in Lum. Lum however has fallen irrevocably in love with him. Now she's living with him, attending his classes, planning their wedding and giving him a dose of her high-voltage electric shocks every time he tries to flirt with another woman (which is invariably). Shinobu is constanly angry with him, Ataru's schoolmates infatuated with Lum want him out of the picture. His parents begin to wish they never conceived him, and a doomsaying buddhist monk lurks around his neighbourhood intent on seeing through Ataru's downfall.
So concludes the first episode of Urusei Yatsura offering but a small glimpse of the what the future might hold for Ataru and Lum. Will Ataru escape his unlucky streak and create the harem of babes he's always dreamed of? Will Lum be able to steer Ataru away from his skirt-chasing ways and win his affections at last? Will Shinobu ever stop fawning after perverted guys like Ataru and find a decent boyfriend? Only time will tell. Things can only get stranger from this point as other aliens from Lum's past drop in and Ataru's bad luck and troublemaking personality continues to attract a continuous parade of obnoxious weirdos.