A dynamical, two-phase flow model in two- and three-space coordinates is presented. The gas-liquid flow is modeled by a Navier-Stokes system of equations in an Eulerian representation. The motion of gas is modeled by a separate continuity equation. The Eulerian approach with UPWIND or TVD discretization and the Lagrangian approach for solving the gas-phase equation are compared with each other on two two-dimensional test problems : the dynamical simulation of a locally aerated bubble column and of a uniformly aerated bubble column. The comparison shows that the results obtained with the TVD-version of the Euler/Euler method and the Euler/Lagrange technique agree quantitatively. On the other hand, it has not been possible to obtain similar agreement even qualitatively with the UPWIND technique, due to the influence of the numerical diffusion effects, which are inherent in the case of UPWIND discretization.