Abstract. -The dynamics of fluid vesicles is studied under flow in microchannels, in which the width varies periodically along the channel. Three types of flow instabilities of prolate vesicles are found. For small quasi-spherical vesicles -compared to the average channel width -perturbation theory predicts a transition from a state with orientational oscillations of a fixed prolate shape to a state with shape oscillations of symmetrical ellipsoidal or bullet-like shapes with increasing flow velocity. Experimentally, such orientational oscillations are observed during the slow migration of a vesicle towards the centerline of the channel. For larger vesicles, mesoscale hydrodynamics simulations and experiments show similar symmetric shape oscillation at reduced volumes V * 0.9. However, for non-spherical vesicles with V * 0.9, shapes are found with two symmetric or a single asymmetric tail.Introduction. -Soft deformable objects such as liquid droplets, vesicles, and cells show a complex behavior under flow. For example, in simple shear flow, fluid vesicles exhibit tank-treading, tumbling, and swinging (also called vacillating-breathing, or trembling) motions, depending on parameters such as shear rate, viscosity contrast, and internal volume [1][2][3][4][5][6][7][8][9]. Understanding the flow behavior of lipid vesicles and red blood cells (RBCs) is not only an interesting problem of the hydrodynamics of deformable, thermally fluctuating membranes, but is also important for medical applications. In microcirculation, the deformation of RBCs reduces the flow resistance of microvessels. In diseases such as sickle cell anemia, RBCs have reduced deformability and often block microvascular flow [10]. Lipid vesicles are considered as a simple model of RBCs and also have applications as drug-delivery systems.The recent development of microfluidic techniques [11] allows the investigation and manipulation of individual