An exact solution of the time-dependent Navier-Stokes equations is obtained for the flow between two eccentric rotating disks executing non-torsional oscillations. An analytical solution described the flow at large and small times after the start is given. The solutions depend on the ratio of the frequency of the oscillation to the angular velocity of the disks and the ratio of the amplitude of the oscillation to the angular velocity and the distance between the axes of rotation. The solutions for the three cases when the angular velocity is greater than, smaller than or equal to the frequency of oscillation are given and discussed. The times required to attain steady flows for the cosine and the sine oscillations are obtained. (C) 2000 Elsevier Science Ltd. All rights reserved.