Beagle brothers fighting

Question
We own two brother Beagles.  They are 10 months old and have been together since birth.  The last few days, they have been fighting with each other and have even drawn blood with bite nicks on their ears.  We don't know how to stop them from fighting.  Would neutering be an answer?  One of them is constantly "mounting" the other which we think he's trying to show his dominance?  Can you suggest anything?

Answer
Sherry, I apologize for the tardy reply. I work for a CPA and this time of year is horribly busy for me. Neutering them both should help some, as it will get rid of the hormone testosterone, which is linked to aggression, but it isn't going to be a quick fix, as they are already entering sexual maturity. It can take up to 6 months for all the testosterone to exit their systems.

What have you been doing when they get into it? What about when one tries to mount the other? When do they fight? Is it over food/toys/you/etc.?