In the first episode, only high-schooler Ataru Moroboshi can stop an alien invasion by playing tag with the gorgeous princess of the invaders, Lum. Against very long odds, he wins, only to find he now has an unexpected wife. While she's away, Ataru accidentally calls a space taxi. The fare: the Earth's entire supply of petroleum!
Just as the Moroboshi family is settling down and coming to grips with the idea that their luckless son has married into an extraterrestrial clan, a peach-shaped package arrives from (literally) out of nowhere, through the large hole it punched through the roof. Mrs. Moroboshi wonders how it tastes. Ataru wonders where it came from. Mr. Moroboshi wonders how he's going to pay off the mortgage now that there's a new repair bill looming. Lum's happy -- it's her infant (but streetwise) cousin, Jariten, or "Ten-chan" for short, coming to live with her and her new husband....
It was a dark and stormy night, and Shinobu is walking home. Suddenly, a spaceship crashes near her, and when she reaches the crash site, finds...a tiger-cow!? Who used to be Lum's fiancée!? And he's usually a stunningly handsome guy!? Can Ataru survive the duel for Lum's love? (Would he want to?) And what happens afterward when the food-obsessed Rei is loosed on an undeserving population of Tokyo with the sum of his Japanese language knowledge being: "Will you cook for me forever?"
The beautiful Crow princess Kurama is awakened by a kiss from Ataru. In accordance with her race's traditions, she must mate with him. Naturally Ataru is more than happy to oblige, but she wants absolutely nothing to do with him.
In part 1, Ataru's brutal new homeroom teacher Kuribayashi has it in for him, and has a Lolita-complex thing for Lum. In part 2, it's Open House Day at Tomobiki High School, and a confrontation between the mothers of Lum and Mendou bring both planets to the brink of interstellar war.
Lum's childhood friend Ran comes to Earth, but she's here to seek revenge on Lum for all times that Lum got her in trouble when they were both little. She also tries to suck out Ataru's youth by kissing him.
Lum's father tricks Lum into coming home in order to hold a matchmaking ceremony for her, where thousands of alien suitors await her. Little did they know that Ataru has found out, and is on his way to the Oni homeworld to crash the party.