An exact solution of the unsteady Navier-Stokes equations is obtained for the now due to a sudden pull with constant velocities of eccentric rotating disks with the same angular velocity. Two different methods are used for large and small times. It is shown that it is convenient to use a Fourier series at large times and an appropriate series expansion after using the Laplace transform technique at small times. It is observed how the velocity field depends on the direction of the constant velocities with which the disks are pulled. (C) 2001 Elsevier Science Ltd. All rights reserved.