The nonlinear rheology of aqueous solutions of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) was investigated. The concentration of CTAB was fixed at 0.1 mol L-1, and the concentration of NaSal was varied from 0.07 to 0.4 mol L-1. For all test solutions, dynamic moduli were described with the Maxwell model having a single relaxation time, tau. Time evolutions of the shear stress, a, and the first normal stress difference, N-1, after inception of the steady shear flow were measured. For solutions having low NaSal concentrations, strain-hardening was observed and sigma and N-1 diverged at a certain strain when the shear rate, gamma (over dot), exceeded tau(-1). For solutions with high NaSal concentrations, stress overshoot similar to that of ordinary entangled polymer solutions was observed at gamma (over dot) between tau(-1) and a certain critical rate, gamma (over dot)(C), while the strain-hardening was observed at gamma (over dot) > gamma (over dot)(C). A simple relationship for elastic solids, N-1/sigma = gamma with gamma being the strain imposed by shear flow, held for all the solutions in the strain-hardening regime. The strain-hardening was attributable to the strain-dependent shear modulus and well described with the network theory considering the finite extensibility of network strands. The segment size of network strands was successfully determined. Thus, the stress-strain relationship obtained after the inception of fast flows is useful for characterizing the network properties.