We examine the dynamics of a thin film of viscous fluid on the inside surface of a cylinder with horizontal axis, rotating about this axis. The stability of the film has been previously explored using the leading-order lubrication approximation, under which it was found to be neutrally stable. In the present paper, we examine how the stability of the film is affected by higher-order corrections, such as inertia (described by the material derivatives in the Navier-Stokes equations), surface tension, and the hydrostatic pressure gradient. Assuming that these effects are weak, we derive an asymptotic equation which takes them into account as perturbations. The equation is used to examine the stability of the steady-state distribution of film around the cylinder (rimming flow) with respect to linear disturbances with harmonic dependence on time (normal modes). It is shown that hydrostatic pressure gradient does not affect those at all, and the effect of surface tension is weak-whereas inertia always causes instability. The inertial instability, however, can be inhibited by viscosity, which can make the characteristic time of growth so large that the film would be effectively stable. (c) 2005 American Institute of Physics.