In this paper a detailed hydrodynamic model for gas-liquid two-phase flow will be presented. The model is based on a mixed Eulerian-Lagrangian approach and describes the time-dependent two-dimensional motion of small, spherical gas bubbles in a bubble column operating in the homogeneous regime. The motion of these bubbles is calculated from a force balance for each individual bubble, accounting for all relevant forces acting on them. Contributions from liquid-phase pressure gradient, drag, virtual mass, liquid-phase vorticity and gravity are considered, whereas direct bubble-bubble interactions are accounted for via an interaction model resembling the collision model developed by Hoomans et al. (1996) to model gas-fluidized beds. The liquid-phase hydrodynamics are described using the volume-averaged, unsteady, Navier-Stokes equations. A preliminary model validation has been performed by comparing the computational results with experimental observations published previously in literature by various authors. The model is shown to predict correctly the motion of a bubble plume in a pseudo-two-dimensional bubble column operated at different superficial gas velocities, provided that a detailed description of the bubble dynamics is incorporated in the model. The effect of bubble column aspect ratio on the hydrodynamic behaviour of the column has also been investigated. Our model predicts the effect of aspect ratio on the flow structure in the bubble column. The importance of the various forces acting on the bubbles will also be discussed and it will be shown that the added mass force and the lift force cannot be neglected in bubble column simulation. Finally, the model has been used to study the start-up behaviour of a two-dimensional bubble column. It will be shown that the history of the gas-liquid two-phase flow significantly affects the flow structure ultimately obtained in a bubble column. This finding has, to our knowledge, not been reported before in literature.