This paper gives a quantitative description of the nonlinear stress relaxation properties of aqueous solutions of entangled rod-shaped micelles. The experimental data of the surfactant system cetyltrimethylammonium bromide-sodium salicylate (CTAB-NaSal) are compared to the theoretical predictions of the single-mode Giesekus model in the nonlinear-viscoelastic regime. Within experimental error, we observed a fairly good agreement between the measured relaxation moduli and the theoretical description with a superposition relation for various deformations. This holds for an anisotropy factor of alpha = 0.5. It was also shown, that the Lodge-Meissner relationship is automatically derived from the Giesekus model. The relaxation phenomena discussed in this paper are of general importance and they are equally observed in different materials such as polymer or protein solutions.