The specification of a communication network requires both a topological and an operational aspect The topological aspect consists of a graph with vertices representing sites and edges their interconnection by lines. The operational aspect consists of calling procedures sufficient to complete various communication tasks. In earlier research, we specified several classes of minimum-time broadcast networks; such networks allow completion of the one-to-all broadcast task from any site as originator in the minimum possible time (i.e., ⌈log₂ n⌉ time units for n sites). Here we present extensions to the operational specifications of one of these classes to realize broadcast networks that are also immune to single site failures and to isolated site failures. In these networks, broadcast incurs the minimum possible delay of at most one time unit for each failing component encountered.