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Two model studies are presented in order to elucidate the effect of confinement on glass forming fluids, attempting to study the effects of the interactions between the confining walls and the fluid particles. In the first model, short bead-spring chains (modelling a melt of flexible polymers) are put in between perfectly flat, structureless walls, on which repulsive potentials act. It is shown that chains near the walls move faster (in the direction parallel to the walls) than chains in the bulk. A significant decrease of the (mode-coupling) critical temperature with decreasing film thickness is found. In the second model, a binary Lennard-Jones liquid is confined in a thin film, whose surface has an amorphous structure similar to the liquid. Although, as expected, the static structural properties of the liquid are not affected by the confinement, relaxation times near the wall are much larger than in the bulk. Consequences for the interpretation of experiments are briefly discussed.