The time evolution, due to dissipative processes, of an initial pattern of poloidal and toroidal mass flows in a tokamak is considered. The calculation is applicable to a collisional, low &bgr;, axisymmetric tokamak of arbitrary minor cross section. Time rates of change of poloidal flows which are subsonic but larger than the diamagnetic speed are given according to the magnitude of the flow and the collisionality of the plasma. Over most of parameter space for typical tokamaks, the poloidal rotation is strongly damped by magnetic pumping at the rate (l/qR)2&ngr;ii, wherelis the mean free path,qRis the ’’connection length,’’ and &ngr;iiis the ion‐ion collision frequency. At higher speeds, even stronger damping is effected by electron thermal conduction. The toroidal rotation is determined largely by the conservation of toroidal angular momentum. A heuristic explanation of the damping due to magnetic pumping is given.