Kimagure Orange Road: Natsu no Mirage (1988)

Based on the manga and anime series Kimagure Orange Road.

Storyline

The protagonist is a young boy named Kyosuke Kasuga. He and his siblings (twin sisters) possess supernatural abilities: telekinesis, teleportation, time shift, etc. The tradition of their family forbids them to use these powers publicly. Whenever they fail to hide their unique nature, the whole family has to move. But now Kyosuke has met a beautiful girl, who is being courted by another guy - a big temptation for him to use the powers...