Parameterized verification of coverability in broadcast networks with finite state processes has been studied for different types of models and topologies. In this paper, we attempt to develop a theory of broadcast networks in which the processes can be well-structured transition systems. The resulting formalism is called well-structured broadcast networks. For various types of communication topologies, we prove the decidability of coverability in the static case, i.e, when the network topology is not allowed to change. We do this by showing that for these types of static communication topologies, the broadcast network itself is a well-structured transition system, hence proving the decidability of coverability in the broadcast network. We also give an algorithm to decide coverability of well-structured broadcast networks when reconfiguration of links between nodes is allowed. Finally, with minor modifications of this algorithm we prove decidability of coverability when the underlying process is a pushdown automaton.