For linear homopolymers the linear viscoelastic predictions of the double reptation model are compared to those of a recent, more detailed model. the "dual constraint model" and to experimental data for monodisperse, bidisperse, and polydisperse polystyrene melts from several laboratories. A mapping procedure is developed that links the empirical parameter K of the double reptation model to the molecular parameter tau (e), of the dual constraint model. thereby allowing the parameter K to be related to molecular characteristics such as the monomeric friction coefficient zeta. Once K (or tau (e)) are determined from data for monodisperse polymers, the double reptation model predicts that for fixed weight-average molecular weight M-w the zero-shear viscosity eta (0) increases slightly with increasing polydispersity M-w/M-n for log normal distributions. while for the dual constraint model eta (0) is almost independent of M-w/M-n. Experimental data for polystyrenes show no increase (or even a slight decrease) in eta (0) with increasing M-w/M-n at fixed M-w, indicating a deficiency in the double reptation model. The dual constraint theory is also applied to hydrogenated polybutadienes and commercial high-density polyethylenes, where we believe it can be used to indicate the presence of long side branches. which are difficult to detect by other analytic methods.