The critical transfer rate of the unsaturated helium 11 film has been measured on surfaces of glass and german silver by a heat conduction method. It is found that a considerable reduction of the transfer rate occurs when the vapour pressure over the film is decreased only slightly below the saturation value. At a given percentage of the saturation pressure, there exists a critical temperature above which film flow will not take place. This critical temperature is shown to be sharply defined, and to decrease with decreasing percentage saturation. At the full saturation pressure the transfer rate is markedly different on the various surfaces used, but as the vapour pressure over the film decreases the flow rate tends to become the same for all surfaces. The critical temperature for onset of superfluidity is also independent of the substrate. The temperature dependence of the transfer rate is different from that for the saturated film, but very similar to the variation found in the flow of liquid through channels of width less than that of the saturated film.