Urusei Yatsura: Stay with You is based on the manga series by Rumiko Takahashi. The protagonist is Ataru Moroboshi, a high school student who accidentally evokes love in the heart of Lum, the princess of an alien demon-like race. The game does not recount the initial events of the manga and instead is built like an episode, assuming the player's familiarity with the general story and characters. Ataru's ex-girlfriend Shinobu disappears under mysterious circumstances. Ataru and Lum must explore the high school building and find out what happened to Shinobu.
The gameplay is that of a traditional Japanese-style adventure, where all interaction (including navigation) is performed by selecting verb commands from a menu and combining them with objects from a list. game progression is fairly linear, and it is typically required to complete an objective in one location in order to be able to proceed to the next one. There are no real puzzles, but an inventory with items that can be examined is present.