Quasi-one-dimensional, two-fluid model conservation equations that allow unequal phase velocities and unequal phase temperatures are formulated by area averaging the time-averaged, local equations over the channel cross section. Two distribution parameters embodying the transverse profiles of the phase fractions and axial velocities appear naturally in the phasic momentum equations as factors in the convective terms. These two parameters can be effectively utilized to maintain hyperbolicity of the macroscopic conservation equation set as is demonstrated by solving a standard horizontal pipe blowdown problem.