We carried out coupled, controlled velocity, magnetic resonance imaging (MRI)-rheometry experiments with colloidal suspensions. For not too high relative velocity of the tools (< 70 rpm), the velocity profiles between coaxial cylinders are composed of two parts: close to the inner cylinder the fluid is sheared at a rate larger than a critical, finite value (in contrast with the behavior of an ideal yield stress fluid) while the fluid is not sheared at all close to the outer cylinder. Even in the steady state the position (critical radius) of the interface between these two regions depends on previous flow history. In particular it decreases with the time of preliminary rest, while the critical shear rate and shear stress along the interface increase because of fluid restructuring in the static region. Using a new MRI procedure the velocity profiles have also been recorded during transient tests. We thus could observe the displacement of the critical radius in time after sudden changes of the imposed rotation velocity. In that case the theological analysis of the velocity profiles show that the effective behavior in the sheared region does not change significantly with velocity, time, or flow history: as a first approximation it can be represented by a simple power-law model with constant parameters. This means that the apparent rheological behavior, i.e., as deduced from usual rheometrical tests without taking into account this discontinuity in shear rate, does not represent the effective behavior of the material. Furthermore, the apparent thixotropy of these fluids might be basically dictated by the displacement of the interface between the sheared and unsheared regions.