A computational framework for dynamic three-phase pipe flow is presented and compared with some severe liquid slugging experiments with air-oil-water flow in an S-shaped riser. The model is based on a hybrid slug capturing and slug tracking formulation, in which a full two-fluid formulation is used in the stratified flow regions. A tracking scheme based on a single liquid momentum balance over the length of the liquid slug is used for the slug region. Slug fronts and bubble noses are tracked with a moving computational grid. This allows for correct reproduction of bubble nose velocities and eliminates numerical diffusion. A mixture liquid momentum formulation for the oil-water mixture is applied, and demonstrated with a simplistic liquid-liquid slip velocity model which includes a gradual transition from separated to mixed oil-water flow. The simulations compare well with the severe slugging experiments, both with respect to pressure amplitude and slugging period. (C) 2013 Elsevier Ltd. All rights reserved.