The objective of this study is to develop a local two-fluid model for the separated two-phase flow pattern, usually referred to as stratified flow, Previous models considered the stratified how pattern as a superimposition of two single-phase hows. However, this assumption is valid for the cases in which the amplitude interfacial waves are small compared to the liquid thickness. In this paper, we propose a complementary approach for the case of thin films in comparison to the wavy region. In this case, a local two-fluid model accounting for the distribution of the two phases is necessary. The paper is based on one such local model of the separated two-phase flow pattern. Since the model does not predict the shape of the gas-liquid interface, we assume it is known a priori. The model accounts for the wavy surface and the interfacial transfer of momentum; this transfer can be induced both by pressure and viscous stress distributions along the wavy gas-liquid interface. In the first part the mathematical development to establish the local two-fluid model of separated two-phase how is presented. In the second part, the adequacy and advantages of simplifying the wave field by assuming a monochromatic dominant wave are considered. The closure conditions for the model are also presented. Interfacial terms of momentum transfer are shown to account for both the shape of the gas-liquid interface and for the distributions of stresses over it. The key feature of the two-fluid model lies in the transfer of momentum at the wavy gas-liquid surface. The transfer of momentum at the gas-liquid interface raises two issues : the first is the deformation of the gas-liquid interface, the second is the distribution of the stresses over a wavy boundary (pressure and viscous stresses). The generation of waves, their deformation and propagation are beyond the scope of this work. Iin the second part of this paper, our goal is to adequately predict the effect of the distribution of the stresses over a wavy boundary for a given shape. In particular, the weight of the pressure term in the transfer of interfacial momentum is estimated.