Drainage displacements in three-phase flow under strongly wetting conditions are completely described by a simple generalisation of well understood two-phase drainage mechanisms. As in two-phase flow, the sequence of throat invasions in three-phase flow is determined by fluid connectivity and threshold capillary pressure for the invading interface. Flow through wetting and intermediate spreading films is important in determining fluid recoveries and the progress of the displacement in three-phase flow. Viscous pressure drops associated with flow through films give rise to multiple filling and emptying of pores. A three-phase, two-dimensional network model based on the pore-scale fluid distributions and displacement mechanisms reported by Oren et al. and which accounts for flow through both wetting and intermediate fluid films is shown to correctly predict all the important characteristics of three-phase flow observed in glass micromodel experiments.