Abstract <p>The flow of a viscous fluid film along the outer surface of a vertical cylinder is considered. For this purpose, a model nonlinear evolution equation for the deviation of the film thickness from the unperturbed level is used. When the region of instability corresponding to a certain azimuthal wave number is narrow enough, a simplified system of equations is obtained from the original equation. It is valid for describing spatially periodic solutions at all wave numbers from the neighborhood of this region. The solutions of this system are presented for several values of the azimuthal wave number.</p>