Elastomers cured with sulfur frequently have improved mechanical properties when the curing conditions are chosen so as to give cross links that consist of chains of Sulfur atoms. If such polysulfidic cross links themselves act as elastomeric network chains, then a bimodal network is produced, albeit inadvertently. Interpretation of its properties requires, accordingly, changes in the description of the network structure, most importantly the replacement of one tetrafunctional cross link by two trifunctional ones separated by a new network chain. Illustrative calculations can be used to elucidate the deformation of such networks in terms of the molecular models much used to characterize simpler, unimodal elastomers. More detailed calculations give results in good agreement with experiment.