Measurements of damping function for step shear up to strain gamma = 5 are here reported for two monodisperse well-entangled polymer melts (polystyrene and polyisoprene). At variance with the classical prediction by Doi and Edwards, which gives an universal damping function for the class entangled polymers, the two measured damping functions are different from each other, and both are less strain thinning than the universal D-E prediction. We compare then our data to a recently proposed theory [Greco, F. Macromolecules 2004, 37, 10079-10088], explicitly accounting for the equilibrium average number n(0) of Kuhn segments in a subchain. In the new theory, different n(0) values lead to different damping functions. It is shown that the independently calculated n(0) values for polystyrene (n(0) = 25) and for polyisoprene (n(0) = 51) lead to damping function predictions quite close to experiments. The number of Kuhn segments between entanglements is then a key parameter to give a consistent picture of polymer dynamics, as far as the nonlinear stress relaxation behavior is concerned.