A six-equation model for a one-dimensional, transient, two-phase flow is briefly discussed, and the characteristic and compatibility equations are obtained by the method of characteristics. The equations consist of five conservation equations and a constitutive relative-velocity equation. The model equations constitute a well-posed initial value problem and have real characteristics in all flow regimes. The ordinary differential equations obtained are suitable for numerical applications, such as for blowdown analyses. The special case of an isothermal unequal velocity model is applied to the case of inflow of a liquid sodium-argon mixture into a horizontal pipe and to the case of pressure pulse propagation rate in an air-water system. The expected S-shaped curves are obtained for the volume fraction of liquid sodium. The numerical results for the pressure pulse propagation agree with experimental data at low-volume fractions.