The results of an experimental investigation of the flow of a highly dilute cationic surfactant solution (tetradecyl trimethyl ammonium bromide with added sodium salicylate as counterion, equimolar 2.4 mM) around a rotating sphere are presented. The flow and the shear-induced phase transition are visualized by means of a Toepler Schlieren optics. The buildup of the shear-induced structures occurs only above a critical shear rate. Once this critical value is exceeded the shear-induced phase separation starts after a characteristic deformation with the shear rate reduced by the critical one. Further analysis of the obtained data is performed on basis of an analytical calculation of the flow around a rotating sphere in a second order fluid (Thomas and Waiters, 1964; Giesekus, 1965). From some characteristic features of the shear-induced structures as induction time and position the parameter describing the elastic properties of the fluid is estimated.