Abstract. -From both NMR and conventional rheometrical data we show that a foam cannot flow steadily below a critical, apparent shear rate and a critical shear stress. At low velocities the shear localizes in a layer of thickness decreasing with the apparent shear rate. When this thickness becomes smaller than a critical value hc (about 25 bubble diameters) the continuum assumption is no longer valid and the apparent behavior in this "discrete" regime differs from the rheological behavior of the foam in the "continuum" regime (for a sheared thickness larger than hc).Concentrated emulsions, suspensions, foams or polymeric gels, of common use in civil engineering, food, cosmetic or pharmaceutical industries, are pasty materials capable to flow only when a sufficiently large stress has been applied to them, a feature associated to their "soft jammed" structure. Since these materials might constitute a new state of matter reminiscent of the glassy state, they are actively studied in physics [1]. Although the solid-liquid transition was initially assumed to be continuous, i.e. the viscosity was considered to progressively tend to infinity as the shear stress decreases towards the yield stress, various recent experimental results with pasty materials have suggested that an abrupt transition occurs at a critical shear rate [2], which leads to shear-banding at low flow rates [3]. Recent theoretical works or numerical simulations [4] providing rheophysical approaches of the behavior of softjammed systems tend to confirm the generic character of such results. Besides, an analogous effect has long been observed with wormlike micellar solutions [5,6], but in that case the different flowing regions were shown to be composed of different phases [7]. For foams, shearbanding [8,9] and fracture [10] under specific conditions at low velocities, or localization of rearrangement processes beyond a critical deformation [11] under dynamic tests, were recently observed. Nevertheless, it is generally considered [10,12] that flows under other conditions are homogeneous and that these materials behave as simple yielding fluids, i.e. with flow rate continuously decreasing to zero as the applied stress decreases to the yield stress. Here we provide a complete set of macroscopic (conventional rheometry) and local (MRI) flow data for a foam. It is shown that foam flows systematically develop shear-banding at low imposed velocities and that the corresponding sheared layer does not exhibit a consistent rheological behavior when the sheared thickness is smaller than about 25 bubble diameters.c EDP Sciences