For some time it has been known that many of the two-phase flow models lead to ill-posed Cauchy problems because they have complex characteristic values. A necessary condition (at least in the linear case) for the Cauchy problem to be well-posed is that it be stable in the sense of von Neumann. For systems of partial differential equations of first order, stability in the sense of von Neumann is essentially equivalent to the condition that the model be hyperbolic (all real characteristic values and complete set of characteristic vectors). Herein models are developed which have real characteristic values for all physically acceptable states (state space) and except for a set of measure zero have a complete set of characteristic vectors in state space. Therefore, these models are hyperbolic a.e. (almost everywhere) in state space. Also, they are stable in the sense of von Neumann a.e. in state space even without inclusion of viscosity terms. The models discussed herein are developed for the case of two-phase separated planar flow and include transverse momentum considerations. These models are referred to as "two-pressure" models because each phase is assumed to exist at an average pressure different from the average pressure in the other phase; the pressure fields are related through momentum considerations. Numerical results on a steady-state problem show good agreement with existing steady-state results. Numerical results on a transient problem agree with a single-pressure model until the onset of numerical instability in the single-pressure model. Compared to the single-pressure (hydrostatic) model, the two-pressure model approximates additional physical features and is shown to be a viable approach for the case of separated flow.