 If you liked
InuYasha
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 ...then you might like
Kamisama Hajimemashita: Kako-hen
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A girl goes back 500 years into the past; people from the past aren't sure if the girl is a human or not; a youkai falls in love with a human woman and tries to become a human too (so they can be together); the girl that goes to the past and the woman the youkai is in love with have something in common