These are a couple of TV series that are part of a franchise that began with an OVA series called Tenchi Muyo! Ryo-Ohki.

Tenchi Universe, on TV Tokyo
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This is a 26-episode TV series, which aired in 1995, in Japan. I saw it in 2000, on Cartoon Network. It has all the same characters as the OVA series, but it's set in a parallel universe or something. I mean, the characters' backgrounds and personalities are basically the same, but the way they all ended up together and what they do once they all meet is different. There are perhaps a few other minor differences, but nothing too serious, though I don't remember it well enough to say any more. I'm sure I get various details confused between this series and the original OVA series. For example, I discovered online that Mihoshi's Galaxy Police partner, Kiyone, was introduced in this series. That really surprised me, because I could have sworn she was in the OVA series. Anyway, Kiyone is much more professional and competent than Mihoshi. She's often exasperated by Mihoshi's incompetence, and would like to be reassigned a new partner, but Mihoshi is totally loyal to Kiyone. Anyway... as with the first series, I'd like to rewatch this someday so I can write a proper review.

There are also a few movies, I guess. So far I've seen one of them, Tenchi Muyo in Love!, which is part of the "Tenchi Universe" continuity, set sometime after the series.

Tenchi in Tokyo, on TV Tokyo
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streaming sites: Funimation; iTunes

This is another 26-episode TV series, which aired in 1997, in Japan. I saw it in 2000, on Cartoon Network. Once again, it has all the same characters, but set in a totally different continuity. There's also another new character, a seemingly normal human girl named Sakuya, who wants Tenchi's affections, which makes all the other girls even more jealous than usual. Another difference in this series involves Ryo-Ohki: in addition to turning into a big, spiky space ship like she does in all the series, she also sometimes turns into a giant pink battle mecha. Anyway, it's my least favorite of the three I've seen, but it's still fun. And I'd like to see it again, to write a proper review.