A binary boundary layer approach is used to analyze the condensation of a saturated vapor on a thin laminar film of either the same or a different liquid flowing over a sphere. It is assumed that the condensate forms a continuous layer on the film. Thus, while the analysis deals with a vapor condensing on an immiscible film, it also applies to a vapor condensing on its own liquid. Expressions are presented for the average Nusselt Number over the segment of a sphere where a thermal boundary layer is penetrating the film and for the degree of utilization of the cooling capacity of the film as a function of the important non-dimensional parameters. Comparison with published data confirms the applicability of the result.