The first normal stress differences N-1 of a highly dilute cationic surfactant solution are investigated in a cone-and-plate rheometer. In continuation of a previous paper (Nowak 1998). where the buildup of a shear induced structure in such a solution was attained after a reduced deformation, the N-1 turned out to be in proportion to the square of the shear rate (gamma )over dot reduced by a critical value (gamma)(c) in a first range above (gamma)(c). At higher shear rates the N-1 tend to lower values than predicted by this relation. Relaxation experiments were performed in the same geometry to determine the characteristic time scales of the shear induced state's decay. In the lower range above (gamma )over dot(c) the stress decay is a monoexponential process, while a second time constant has to be introduced to describe the relaxation in that range, where the N-1 deviate froth the parabolic dependence of the reduced shear rate.