The electronic structure of a -network polymer with random numbers of two types of monomer units is considered in a "conjugated circuit" resonance-theoretic framework. A transfer-matrix technique for computing relevant ensemble-average energies is described and applied to a few example simple benzenoid systems. A type of long-range ordering is noted to be relevant, and some of its implications are discussed. 1987 J.C. Baltzer AG, Scientific Publishing Company.