  We study the stationary states of networks consisting of weakly coupled
bistable units. We prove the existence of a high multiplicity of stable steady
states in networks with very general inter-unit dynamics. We present a method
for estimating the critical coupling strength below which these stationary
states persist in the network. In some cases, the presence of time-independent
localized states in the system can be regarded as a `propagation failure'
phenomenon. We analyse this type of behaviour in the case of diffusive networks
whose elements are described by one or two variables and give concrete
examples.
