Flow birefringence and dichroism experiments are used to study the behavior of solutions of a hydrophobic ethoxylated urethane with a molecular weight of 35 000 g/mol and a C16 hydrophobic end cap in a concentration range around C*. Relaxation experiments after step shear have shown the existence of two relaxation processes. The first relaxation process with a characteristic time, tau(short) approximate to 0.1 s, independent of concentration, has been attributed to the lifetime of an end group in a micelle and subsequent relaxation through a Rouse process. The second relaxation process (tau(long) approximate to 300 s), has been attributed to the relaxation of aggregates of polyoxyethylene chains. They induce a small dichroism in the solutions and damped oscillations in start-up shear flows at low-shear rates. Upon cessation of steady-shear flow, the two relaxations are still observed, the amplitude of the short time one increasing with shear rate. The origin of this long-time relaxation, which is not observed in classical rheological measurements, is attributed to the presence of organic impurities remaining from the chemical modification of the polymer. Extensive purification of the polymer leads to the disappearance of these impurities and consequently of the long relaxation process.