Attempts to measure rheological parameters at interfaces have long been hampered by an inadequate hydrodynamic analysis of the fluid motion involved. The present study has been founded upon a careful mathematical analysis of the surface analogue of the Couette viscometer. Here the assumption of incompressibility of the film has been used, but because counter rotating, coaxial rings or disks inserted into a fluid interface supporting a monomolecular film do not in the limit of slow rotation generate compressive stresses, the limitation is not a serious one.