We carried out systematic rheometrical tests under controlled stress with smooth and rough parallel disks, along with magnetic resonance imaging (MRI) tests in coaxial cylinder geometry, with foam and a model concentrated emulsion. At low shear stress wall slip appears to occur but the bulk fluid remains static, as proved by the fact that in this regime the apparent shear rate obtained for a given shear stress is inversely proportional to the gap between the disks. At high shear stress data with different surface types and gaps coincide, suggesting that wall slip is negligible in this regime. In parallel, MRI results show that, in contrast with the apparent, simple, yielding behavior observed in usual rheometry, there is an abrupt transition from a finite shear rate to a static one at critical stress. This critical shear rate precisely corresponds to the transition between the two regimes of slip. This suggests that different flow regimes occur with these materials: (1) at low stress, with smooth surfaces a layer of a different material is sheared along the solid surfaces whereas the rest of the fluid does not flow; with rough surfaces there is no flow; (2) beyond a critical stress, for both surface types, the bulk fluid starts to flow but the shear is localized in a thin layer; then the thickness of this layer increases when stress is applied; (3) for both surface types homogeneous flow is obtained only beyond slightly larger stress, which is associated to a critical, apparent shear rate. (C) 2003 The Society of Rheology.