Tenchi Muyo! Ryo-Ohki
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This is an OVA series, the first series in the Tenchi Muyo franchise ("Tenchi Muyo" translates as "No Need For Tenchi.") Actually, it's a series of series. The first OVA series of seven episodes was released in Japan from September 1992 to September 1993. The second series of seven episodes was released from September 1994 to September 1995. These first two series were aired on Cartoon Network in July 2000, which is when I saw them. A third OVA series of seven episodes was released in Japan in 2003-05, and a fourth series of four episodes in 2016-17. I haven't seen either of those series. (I've also seen a couple of Tenchi Muyo TV series, and I probably have some details of the OVAs and TV shows mixed up in my memory.)
The main character is a teenager named Tenchi Masaki, who lives in Okayama, Japan, with his grandfather. Um, in at least one series his grampa is called Katsuhito, but his real name is Yosho. He is from the royal family of planet Jurai, which Tenchi will become aware of in the course of the series. He came here like 700 years ago and fell in love with a human woman and married her. Now, um... Tenchi's dad is Noboyuki. He's kind of clueless. He was married to Yosho's daughter, who died when Tenchi was young. In the present, Tenchi is surprised by the arrival on Earth of several cute girls from outer space. They include Princess Ayeka and her little sister Princess Sasami, from Jurai; a space pirate named Ryoko (who is my favorite of the girls); a Galaxy Police officer named Mihoshi; and Washu, the greatest genius in the universe! (Washu is my second favorite; she's insane, and kind of evil, but fun.) Ayeka's a total... princess (and not in a good way). But she's still a friend and basically a decent person. Sasami is just this cute little kid who's the most sensible and helpful of the bunch. She does all the cooking and a lot of the cleaning and she's very friendly. Mihoshi is a total ditz and clumsy and annoying. She'd rather watch fictional Space Police on TV than actually do any police work herself, although she does try, but she's pretty inept. Anyway, Ayeka was supposed to marry her half-brother Yosho 700 years ago, but he disappeared. She came to Earth looking for him, but now she falls in love with Tenchi. All the girls do. Or most of them, anyway. But Tenchi isn't interested in being more than friends with any of them, so their attention embarrasses him. Also there is a cabbit named Ryo-Ohki who is extremely cute and adorable. (Cabbits are basically space rabbits that sound more like cats, and can transform into big, spiky space ships. And I have a plush one.) You'd think with her name in the show's title, Ryo-Ohki would be the most important character, but as far as I can tell, she's not of any great importance. Anyway, it's a terribly funny show and they all have plenty of strange adventures and stuff. Maybe someday I'll get a chance to rewatch the series and say more about it... and also see the other series of OVAs.