 If you liked
Xenosaga The Animation
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 ...then you might like
Divergence Eve
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Both this anime have aliens that invade from a different space time by human using some kind of object which is not necessary to use. The alien act very similar too.
In Xenosaga there is a android woman who posses mysterious powers while in Divergence Eve there is a girl with supernatural power. That is also similar because both of them have some kind of superpower.