The influence of the interfacial pressure and the flow distribution in the one-dimensional two-fluid model on the stability problems of interfacial waves is discussed. With a proper formulation of the interfacial pressure, the following two-phase phenomena can be predicted from the stability and stationary criteria of the interfacial waves: onset of slug flow, stationary hydraulic jump in a stratified flow, flooding in a vertical pipe, and the critical void fraction of a bubbly flow. It can be concluded that the interfacial pressure plays an important role in the interfacial wave propagation of the two-fluid model. The flow distribution parameter may enhance the flow stability range, but only plays a minor role in the two-phase characteristics. (author). 20 refs., 3 tabs., 4 figs.