substrate, we consider an axisymmetric liquid film on a horizontal cylindrical surface subjected to axial harmonic oscillation in the high-frequency limit. The nonlinear evolution equation describing the nonlinear dynamics of this physical system in terms of the averaged film thickness derived and analyzed. The method used for the derivation of the evolution equation is based on long-wave theory, the separation of the relevant fields into fast and slow components and asymptotic expansions. The linear stability analysis in the framework of the derived evolution equation for a film of a constant thickness is carried out. It shows that axial forcing of the cylinder may result in either stabilization or destabilization of the axisymmetric flow with respect to the unforced one, depending on the choice of the parameter set. The results obtained from the linear stability analysis have been compared with the behavior of the unforced system which is intrinsically unstable, in terms of the cutoff wave number and the growth rate of disturbances. For specific fluids chosen here as water-glycerin solutions and for a fixed mean film thickness, it has been found that it is possible to stabilize an axisymmetric film coating on a cylindrical surface in a certain range of the ratio between the radius of the cylindrical substrate and the mean thickness of the film for normal modes of all wave numbers. This range of stabilization depends on a set of forcing parameters. One of the reasons for such stabilization is due to a liquid inertia associated with the forcing imparted on the film via the boundary. On the other hand, the same parameter set could be also destabilizing for a cylinder of a different radius. Hence fast harmonic axial forcing of a cylindrical substrate may be a feasible tool for manipulating an unstable character of a liquid film on a static cylinder, making it either stable or even more unstable by increasing the growth rate of disturbances and/or by widening the range of linearly unstable modes. It is also important to note that the results of the linear stability analysis carried out here are valid for small wave numbers of the normal modes with respect to which stability properties of the system are studied.