I have two nurtered brother cats and my girlfriend has two nuetered cats also?

I am not one to separate cats when a new cat is being brought home since the getting together will just be prolonged, however since there a 2+2 you may want to keep the new arrivals in a room by themselves for a few days or longer and stroke your gf's cats with a soft cloth to get their scent on it and let your cats investigate the new scent. They will know that there are other cats in the house and when they do get together there will be the "alpha" cat establishing in your home. There will be the "hissy-spitting,paw slapping and downright throw downs. It will take time and patience for the cats to establish what the pecking order is and when the throw downs get to rough a spray bottle with water sometimes will help. The cats will figure this out amongst themselves and the longer they are separated the longer it will take. Some may suggest that you keep the new cats in a cage kennel, not a fan of that though, and let the 4 cats explore each other that way. TIME and patience is usually what works in my house. I hope this is of some help to you and at some point they will most likely just TOLERATE each other.