The shear-thickening transition in dilute surfactant solutions is inve
stigated using rheology and small-angle neutron scattering. Steady she
ar experiments on a new thickening system, the tosylate of cethyltrime
thylammonium, revealed a continuous increase of the apparent viscosity
above a critical strain fate (gamma)over dot(c). Concentration and te
mperature variations of (gamma) over dot(c) are derived, and the forme
r is found to be in contradiction with a theoretically predicted gelat
ion. From the scattering under shear, we establish a clear correlation
between flow and structure. In the thickening region, the patterns ar
e due to the superposition of two coexisting states, one viscoelastic
entangled sheared network and one still purely viscous made of short a
ggregates. At higher (gamma) over dot(c), the former state dominates a
nd its increasing orientation results in shear-thinning.