A fluid drop placed on a plane surface will spread until the slope at the edge of the drop reaches its equilibrium value. If the plane is inclined, the drop will slide down the plane as well as spreading. To study these time-dependent motions, it is necessary to make some hypotheses about the conditions at the edge of the drop. The solutions presented here are obtained on the basis of the slip boundary condition near the edge and of a constant contact angle. The drops are assumed to be thin enough for lubrication theory to be valid and they are also assumed to be two-dimensional. With these restrictions, it is possible to trace the changes in shape of sliding and spreading drops. The concept of a velocity-dependent apparent contact angle is examined.