Heat or mass transfer is considered in a failing laminar film with a parabolic speed profile. The speed profile is determined by gas flow at the film's free surface. Exact analytical solutions have been obtained for temperature or concentration profiles under general boundary conditions of the third kind, as well as for the corresponding Nusselt (Sherwood) numbers. The two cases of most practical importance are discussed in more detail: (I) heat or mass transfer with the wall and (II) mass transfer with the gas. Subsequent analysis of the solution has resulted in good approximate formulas for these two cases.