Flow behavior was examined for a 1.0 wt % aqueous solution of hydrophobically modified ethoxylated urethane (HEUR; M(w) = 4.6 X 10(4)). In the linear viscoelastic regime, the solution exhibited single-Maxwellian behavior attributable to thermal reorganization of the transient network composed of strings of HEUR flower micelles. Under shear flow at intermediate shear rates just above the equilibrium relaxation frequency 1/tau, the solution exhibited thickening characterized by monotonic increase of the viscosity growth function eta(+)(t;(gamma) over dot) with time t above the linear eta(+)(t) and by the steady-state viscosity eta((gamma) over dot)) larger than the zero-shear viscosity eta(0). However, at those (gamma) over dot, the first normal stress coefficient growth function Psi(+)(1)(t;(gamma) over dot) and its steady-state value Psi(1)((gamma) over dot) remained very close to the linear Psi(+)(1)(t) and Psi(1,0) and exhibited no nonlinearity. In addition, the relaxation times of the viscosity and normal stress coefficient decay functions eta(-)(t;(gamma) over dot) and Psi(-)(1)(t;(gamma) over dot) measured after cessation of steady flow agreed with those in the linear regime. All these results suggested that the network strands were just moderately stretched to show no significant finite extensible nonlinear elasticity (FENE) effect and that the number density 11 of the network strands was negligibly affected by the shear at (gamma) over dot just above 1/tau. A simple transient Gaussian network model incorporating neither the FENE effect nor the increase of v suggested that the thickening of eta(+)(t;(gamma) over dot) and eta((gamma) over dot) and the lack of norffinearity for Psi(+)(1)(t;(gamma) over dot) and could result from reassociation of the HEUR strands being in balance with the dissociation but anisotropically enhanced in the shear gradient direction.. In contrast, at (gamma) over dot >> 1/tau eta(+)(t;(gamma) over dot) exhibited overshoot above the linear eta(+)(t) and then approached q((gamma) over dot) < eta(0), whereas Psi(+)(1)(t;(gamma) over dot) stayed below the linear Psi(+)(1)(t) and approached Psi(1)((gamma) over dot) << Psi(1,0) after exhibiting a peak. The relaxation of eta(-)(t;(gamma) over dot) and Psi(-)(1)(t'(gamma) over dot) after cessation of flow was considerably faster than that in the linear regime. These nonlinear thinning features at (gamma) over dot >> 1/tau were attributable to the flow-induced disruption of the HEUR network (and decrease of v).