The transverse velocity component, the growth of the boundary layer and the transverse curvature cause self-induced favorable pressure gradient for the flow on a rotating circular cylinder in an axial flow. When the external pressure gradient is adverse, the effect of this favorable pressure gradient influences boundary layer separation and also the flow development downstream of this separation point. The types of post-separation behavior can be classified into several flow patterns varying with the ratio of the transverse surface velocity to the typical axial velocity. In this paper, by perturbing the solution for some surface velocity, the solution for slightly different surface velocity is obtained and the influence of change of the surface to typical axial velocity ratio is investigated. The first-order and second-order perturbations are calculated and it is shown that the change of flow pattern can be predicted by the present perturbation method.