The velocity lag between the two discs in the eccentric disc rheometer, inertia effects being ignored, has been studied theoretically. It is shown that the assumptions made in literature, viz. a constant velocity gradient between the discs, violates the momentum balance. Applying the principle of conservation of momentum to a velocity field of the form suggested by Blyler and Kurtz, but in which the velocity gradient is a function of the distancezto the lower disc, one can determine analytically the velocity field for a Newtonian liquid. For a general viscoelastic fluid a solution can only be given under certain restrictions. For the velocity field found the momentum balance is satisfied. The energy dissipated in the sample is supplied by the upper (driven) disc, as it should be. The energy balance, however, is only satisfied to first approximation. The experimental measurements of Davis and Macosko are in good agreement with the present theory. This is not the case with the experimental data given by Payvar and Tanner.