Flow and diffusion of water in natural porous media, quartz sand, and calcareous gravel were measured using a 1.5-T clinical magnetic resonance tomograph. The spatial resolution of the dynamic measurements was 1.32 x 1.32 x 5 mm3, and the time between two cross-sectional measurements was approximately 10 s. The measured coefficients of molecular diffusion for water were in good agreement with theoretical data. Flow was measured without any tracer at velocities between 0.15 and 6.67 mm/s. The results, based on a calibration within one part of the column, were in good agreement with data obtained from a tracer experiment and from a numerical model. It was possible to measure the flow velocity in larger pores and preferential flow paths directly. The results of the flow measurements in smaller pores reflected the mean velocity within that volume element. In that case the obtained values were close to the average linear velocity. Since the time resolution is high a monitoring of flow processes is possible. The pore space was imaged with a spatial resolution of 0.5 x 0.5 x 0.5 mm3. Here, the porosity of pores that are larger than 0.2 mm can be measured directly; for smaller pores a calibration is necessary.