The nonlinear rheology of an aqueous wormlike micellar system made of cetyltrimethylammonium chloride with sodium salicylate is studied in this work. At high NaCl salt concentration the rheological measurements show a Maxwell behavior for all the solutions. The data of these samples are analyzed with respect to the Spenley, Cates, and McLeish model. The dimensionless quantities sigma(plateau)/G(0) and gamma c tau(R), which characterize the nonlinear rheology are compared to the predictions of this model. At a fixed surfactant concentration these quantities are found to be insensitive to changes in salt concentration and in temperature, respectively. The experimental value of the ratio sigma(plateau)/G(0) we find is close at hand to the theoretical one. A discrepancy between the theory and the experiments occurs,;however, in comparing the Weissenberg number defined by the product gamma c tau(R).