Urusei Yatsura (1981)

Grab her horns and she might just become your darling!

The invasion of an alien race known as the Oni begins a new life for Ataru Moroboshi, a lecherous trouble-making tenth grader in the small town of Tomobiki. After unwittingly proposing to the Oni princess Lum Invader instead of his sweetheart Shinobu, Ataru becomes a conduit for aliens arriving on Earth, causing all sorts of havoc for him and his companions, not to mention his own reputation!