The effect of shear on a lyotropic lamellar phase is studied by the means of small-angle light scattering and direct microscopic observations. We found a complex behavior that can be described by a shear diagram. This diagram exhibits successively as a function of shear four different steady states. After a transition to a phase of monodisperse multilamellar vesicles with no long-range order there is a transition to the same vesicles exhibiting long-range order. At even higher shear rates, there is a transition between this ordered population of vesicles of size typically 1 mm to another ordered state made of vesicles which are much bigger (from 10 to 50 mm). [S0031-9007(97)02380-6] PACS numbers: 64.70. Md, 61.30.Eb, 82.20.Db Recently, it has been shown that the effect of shear on both lyotropic and thermotropic lamellar phases can be described by a shear diagram describing a succession of stationary states of orientations separated by dynamic transitions [1][2][3]. In the first system studied [2], the shear diagram exhibited three different orientation states. At very low shear, a partially oriented state with the normal to the smectic layers mainly parallel to the shear gradient direction was observed until a transition to a state of monodisperse multilayered vesicles (named spherulites) was observed (around 1 s 21 ). At even higher shear rate (10 1000 s 21 depending upon the lyotropic sample) another transition was observed between the state of vesicles to another oriented state with no defect in the direction of the flow but some defects remaining in the vortex direction. The connection between the rheological properties of the lamellar phase and the shear diagram has been made [4].More recently while studying a different system, another type of transition has been observed. In the multilayered vesicle state, a layering transition has been observed [5] similar to the shear ordering transition observed in colloids [6]. Indeed, in increasing the shear rate, the multilayered vesicle state that does not exhibit any long-range order between the vesicles spontaneously orders under shear to show a long-range order of layers of vesicles sliding on each other.We report here a more complex behavior observed on a lyotropic lamellar phase. In addition to the transitions previously described as a function of shear, this system exhibits a new transition between two states of ordered multilayered vesicles. These two states can be easily differentiated by the vesicle size, and the transition between these two states is observed as a jump from small to big vesicles when either the shear rate or the temperature is increased. This transition which is in general discontinuous becomes continuous above a critical temperature. The shear diagram of this system is established.The system studied is a quaternary lyotropic lamellar phase which phase diagram has already been published [7]. It is composed of water, sodium dodecyl sulfate (SDS), octanol, and sodium chloride. One unique sample has been studied whose composition is, respe...