The dynamic phase diagram of triethylene glycol dodecyl ether (C12E3) in D2O was determined for 40, 50, and 60 wt % of surfactant. The shear flow effect on the nonionic lamellar phase was investigated as a function of temperature and concentration. The transition from planar lamellae (L-alpha)-to-multilamellar vesicles (MLVs) was characterized by means of rheology, rheo-small-angle neutron and light scattering. New insight into the nature of the transition region between L-alpha and the MLVs state is provided. A disorder-order transition was also observed by SANS. This is attributed to a transition from disordered MLVs to a close-packed array of MLV's with slightly higher order than before. Moreover flow instability was observed in the shear-thickening regime at 40 degrees C.