 If you liked
Elfen Lied
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 ...then you might like
3x3 Eyes
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The overall mood in each of these anime is dissimilar, but they share lead female characters that go from dangerous, and even evil, to sweet and completely innocent in a heartbeat. Both series are violent, Elfen Lied being much more so. Both anime develop a romantic relationship involving an ordinary boy and an extraordinary girl. 3x3 Eyes has a supernatural element that is absent in Elfen Lied's more realistic setting. The split personality of the main characters, and the problems they cause is the main reason to justify this recommendation.
All I have to say is that Yakumo and Nana take serious abuse! If you can handle the large amounts of blood and gore and the occasional down time filled with slice-of-life drama, then Elfen Lied will do you just fine.
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Recommended by tranceotaku
Both main characters have split personalities. Both have different species from humans (Diclonius, 3 eyed demons)
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Recommended by Aurora3500