Do you know what anime is this? (There were spaceships, or something similar, and two girls, and lot more)?

This sounds a lot like Kiddy Grade. You can look it up on Wikipedia and check to be sure, there should be pictures of it. I do remember the episodes with a lot of them and such. Give it a show and test it out. It did involve space and all that as well. The red head was named Eclair and the white haired girl was Lumiere.