RahXephon

In the year 2012 Japan was invaded by the Mu. Human-like beings from another dimension with blue blood. In the year 2015 Tokyo is attacked by invaders, who are repelled by a humanoid weapon called a Dolem. During the chaos, Ayato Kamina meets Reika Mishima, a classmate. During that same day, he is attacked by government officials but a woman named Haruka comes to his rescue, informing him that she was sent to get him by the Organization TERRA, and that Tokyo had been sealed in a time rift where time flows one third as fast as the outside world....