We consider a pair of networks A and B which are subject to failures of their components. In A, edges are subject to failure, and A fails when it disintegrates into several isolated clusters each containing a single terminal. Edges of A fail in random order and their failure moments follow Poisson process. After A has failed, terminal α of A causes a failure (”attacks”) on Rα randomly chosen non terminal nodes of network B. All edges incident to an attacked node are erased. The ”attacks” take negligible time. Network B failure takes place if it loses its terminal connectivity. We study the probability that B will be in failure state at moment t as a function of t and R = ∑ Rα The main formal tools which we use are the D-spectra (signatures) of networks A and B and de Moivre’s combinatorial formula.