Manatsu no Eve is the second Tenchi Muyo movie, which came out in '97--while it's only sixty minutes long, I rewatched it again recently and enjoyed it. Manatsu no Eve takes the Tenchi Muyo cast that's familiar to a lot of anime fans and adds Mayuka, a mysterious girl who appears one summer day and claims to be Tenchi's daughter. What happens from there is a good mix of drama, action, and comedy as the cast reacts to the new arrival--Ryoko doesn't trust her and thinks she's out to kill Tenchi, Ayeka worries about losing Tenchi to her, Sasami's excited to find a new playmate, Washu sees a new research subject, and Tenchi himself is just overwhelmed (as usual).
If you're not familiar with Tenchi Muyo, it's a prototypical harem series--you have the main character, Tenchi, who thinks he's an ordinary high school student, but finds out his grandfather is really royalty from a planet called Jurai. Since he has Juraian blood, Tenchi has corresponding l33t powers, and through various events he finds himself living with a bunch of girls vying for his attention: Ryoko, former space pirate, Ayeka, ojou-sama princess of Jurai, Sasami, Ayeka's younger sister, Mihoshi, the most airheaded galaxy police detective ever, Washu, the brilliant mad scientist, and Kiyone, Mihoshi's hapless partner. Since most average high school guys would kill to be in Tenchi's place, it figures the series became very popular. None of this is really explained in Manatsu no Eve, it assumes you're familiar with the cast and the premise going into it. There's a Wikipedia entry that explains all the various Tenchi Muyo canons (yes, there's more than one) and spinoffs--Manatsu no Eve is the second movie, but has no tie-ins to the first one at all since it's in the OVA timeline (sort of) and the first movie was more a sequel to the TV series.
Manatsu no Eve starts out with a flashback to the midsummer Startica festival on Jurai, which is similar to Christmas, or more precisely Chrstimas in Australia since it's summer. A little boy who we later learn is Yosho is standing under a tree, waiting to meet someone. The camera cuts to a little girl who runs up, obviously excited to see him, and gives him a present, a small box that shows a hologram of a Christmas tree. But a moment later the Juraian version of a SWAT team shows up, grabs Yosho, and while he protests they attack the girl, knocking her to the ground and beating her as Yosho screams for them to stop. One of the SWAT team members cuts her in half with his sword, and we see she's not a normal girl, she's a demon from the world of darkness...then with a cry of anguish and anger she disappears...
Cut to the present, and Yuzuha, the demon/little girl, waking up in her room--she sees a scene Tenchi and the rest of the cast celebrating Christmas, and she gets an idea. She steals some of Tenchi's hair, and throws it in a vat with some of hers, chuckling that in a few months she'll be sending a midsummer Startica present to them...
That summer, it's an everyday scene at the Misaki household, meaning Tenchi's harem are doing chores, with the noteable exception of Ryoko, who's just getting up even though it's probably noon. Tenchi's tending his mother's grave near the Misaki shrine, but on his way home on the temple steps he runs into a blue-haired girl he'd never seen before--and to his shock she calls him 'Papa' (even though she looks about as old as he does), and follows him home. Ryoko and Ayeka are not amused that the mystery girl, who's named Mayuka, is clinging to him, and it's pretty funny to see both of them with more or less the same reaction. Mayuka says she knows Tenchi is her father, but doesn't remember anything else. Washu pulls out a strand of Mayuka's hair, in typical Washu fashion, and analyzes it--and confirms Mayuka really is Tenchi's daughter, possibly from the future, although Washu's having trouble figuring out who the mother is.
From there, Mayuka goes on to make friends with Sasami and the others, with the exception of Ryoko, who's convinced she's up to no good...and soon it looks like Ryoko may be right...
Manatsu no Eve has its faults, but overall I liked it--it has the same feel as the OVA series and lets you see the cast in a different light. Ryoko and Ayeka even have a serious conversation at one point, which is something that's a little rare in the Tenchi universes otherwise, where normally they're just fighting like feral cats. Mayuka and Yuzuha are both interesting characters--Yuzuha is an evil monster on the one hand, but she seems to have very human feelings at times too, and it's hard not to feel bad for her. To me Mayuka came across as likable and sincere, even in the face of not knowing her own past or what was really happening to her.
Manatsu no Eve may not have the animation budget of the first Tenchi movie, but it still looks good, even by today's standards. A few of the scenes really stand out, like the Startica flashback in the beginning--the sudden transition from two kids sharing a moment of awe at a festival to the violent arrival of the SWAT team was done really well. The dramatic scenes are intense, all the more so if you're familiar with the characters from watching the OVA or TV series. I really liked the movie's atmosphere, with very detailed backgrounds at times, and background music that always seemed to be perfect for the scene. The movie's only 60 minutes long, which isn't a lot of screentime to work with, but they did a good job fitting everything in and still telling a complete story. More background on Yuzuha would have been nice, or more screentime for Mihoshi and Kiyone, but with just an hour to work with it would've detracted from the main story to do that. In the end, it tells a solid story, and the epilogue that plays out over the ending credits is a nice touch.
Flaws? Well, it seems too convenient that Washu always comes up with a way to save the day on next to no notice (like the 'Jurai energy generators' from the first movie). And some may not like Mayuka, especially if your favorite character is one of the ones that gets little to no screentime.
If you're a fan of Tenchi Muyo I think Manatsu no Eve is worth watching (although since it came out so long ago you've probably watched it already in that case), but even if you aren't a Tenchi fan you won't really be lost since it's a self-contained story. Comparing the quality of the animation and the direction to some more recent series, I think Manatsu no Eve stacks up pretty well, so don't let the 1990s release date scare you off.