Summary: Consider a network in which \(n\) processors are connected by communication lines and are allowed to communicate with at most one other processor at a time. Broadcast is the task of transmitting a message originated at one node to all other nodes in the network. Presented in this paper is a broadcasting scheme that can tolerate up to \(k\leq\lfloor\log n\rfloor\) line failures; that is, it assures that each node in the network will receive the message from the originator when up to \(k\leq\lfloor\log n\rfloor\) lines are faulty. The time required by the broadcast protocol is minimum, except in some cases that might require one unit of time more than the minimum. Moreover, an algorithm for constructing networks supporting the broadcast scheme and having approximately the minimum possible number of lines is given.