We consider the dynamics of a drop with a pinned contact line , as described by the thin film equation . Starting from an arbitrary initial condition at , the profile relaxes toward an equilibrium parabolic profile. Our focus is on the early-time dynamics, which for is described by a local similarity solution. As a result, the contact angle changes like a power law as a function of the time . In the case , which corresponds to a no slip boundary condition, the problem becomes non-local, and the change in contact angle is of the form (with complex). We consider the implications of this result for Huh and Scriven's contact line paradox for the case . (joint work with Marco Fontelos)