Nuclear magnetic resonance (NMR) imaging (MRI) was used to investigate the flow behaviour of PTFE pastes and other highly viscous fluids in a new Couette shear device, developed especially for pastes. The mean moisture contents of the PTFE pastes were between 35 and 55%, the normal stress varied between 0 and 5 bar. By means of MRI the local moisture in the material, the deformation and velocity profiles of the investigated specimens can be determined non-destructively and contact-free. The results are in part contrary to known ideas and cannot be satisfactorily explained. We believe that the application of the shear device, and perhaps of shear experiments in general, is problematic in the use of disperse, to phase-separation tending systems. Velocity profiles and, hence, in combination with the torque necessary for rotation of the inner shaft, flow functions and possibly wall slip functions can in principle be determined for highly viscous quasi-homogeneous materials by means of MRI. The main purpose of the investigations, however, is not to determine flow functions with a new technique. But rather unexpected, often disturbing phenomena of disperse solid-fluid systems in Couette devices shall be presented.