A detailed theoretical study of unsteady free convection boundary-layer flow near the stagnation point of a two-dimensional cylindrical surface embedded in a fluid-saturated porous medium is presented when the surface temperature oscillates about a mean value above ambient. Both numerical and asymptotic solutions are employed to solve the governing equations for general values of the frequency omega and amplitude A of the surface temperature oscillations. Results for the heat transfer rate, boundary-layer thickness and temperature profiles are obtained for both small and large Values of A and also for slow and fast oscillations. It is found that outside the thin boundary layer on the surface, a steady flow is induced for large times and fast oscillations. This steady boundary-layer flow is studied in detail for large values of the amplitude A.