Broadcast networks are often used in modern communication systems. A common broadcast network is a single hop shared media system, where a transmitted message is heard by all neighbors, such as some LAN networks. In this work we consider a more complex environment, in which a transmitted message is heard only by a group of neighbors, such as Ad-Hoc networks, satellite and radio networks, as well as wireless multistation backbone system for mobile communication. It is important to design efficient algorithms for such environments. Our main result is a new Leader Election algorithm, with O(n) time complexity and O(n*lg(n)) message transmission complexity. Our distributed solution uses a propagation of information with feedback (PIF) building block tuned to the broadcast media, and a special counting and joining approach for the election procedure phase. The latter is required for achieving the linear time. It is demonstrated that the broadcast model requires solutions which are different from the known point-to-point model.