Why do my parakeets (aka budgies) attack each other during breeding?

My two parakeets (a boy and a girl) mated and laid a few eggs. About three times a day, they fight and sometimes get hurt (not fatally, thankfully). The male is bleeding on the cere. Yesterday, I looked in and saw that the female had a bleeding scratch to the right of her beak. Why is this happening? I'm really worried that one of them will kill the other or something. Help!!!!