We obtain evolutionary equations for non-stationary viscous accretion discs in which particles are orbiting along Keplerian ellipses that are slowly drifting towards the centre. It is shown that, for any reasonable viscosity law, stationary accretion is possible, with all orbiting particles moving with the same eccentricity. We investigate the stability of circular discs with respect to eccentric particle motion and find that instability develops for some viscosity laws. In particular, we show that formal application of the α-prescription for the viscosity leads to instability