A model has been derived for interfacial wave propagation for a liquid film on the wall of a vertical pipe and for a flowing gas in the central core. An analytical study is presented for the stability of a flat interface, and for traveling waves on the interface. Long wave theory is applied to both phases and the resulting conservation equations are of the same form as a two-fluid model. Two situations are examined: the interface between a Taylor bubble and the liquid film, where the gas velocity is small, and the interface for cocurrent annular flow where the gas velocity is relatively large. The interface between a Taylor bubble and a liquid film was found to be dominated by waves, which can be destabilized by the inertia of the liquid phase. For annular flow the interface is subject to a Kelvin-Helmholtz instability. When the gas flow rate is small, and surface tension is negligible, the traveling wave has a shape similar to that of a Taylor bubble except near the tip and trailing edge. When surface tension is dominant, the solution is a soliton. This region and the receding part of the soliton appears to be related to the ripple waves seen near the trailing edge of Taylor bubbles. (C) 2004 Elsevier Ltd. All rights reserved.