I assume these are text messages you're talking about. Are you using the same Apple ID on both phones? Look in Settings -> Messages -> Receive At. If you're logged in to, and receiving messages from, the same Apple ID, any text messages sent via Messages to that e-mail address will be duplicated across both devices.
Also, note that you posted this in the forum for discussing Mac OS X 10.7, on Mac computers. The iPhone experts hang out over on the iPhone forum. I have asked the hosts to move it to there, but you should be aware of where that is in the future.