Abstract. -Using molecular dynamics simulations we investigate the relaxation dynamics of a supercooled liquid close to a rough as well as close to a smooth wall. For the former situation the relaxation times increase strongly with decreasing distance from the wall whereas in the second case they strongly decrease. We use this dependence to extract various dynamical length scales and show that they grow with decreasing temperature. By calculating the frequency dependent average susceptibility of such confined systems we show that the experimental interpretation of such data is very difficult.Motivation. -The details of the mechanism giving rise to the dramatic slowing down of the dynamics of glass-forming liquids upon supercooling are still unknown (see, e.g. [1]). Although the mode-coupling theory of the glass transition allows to rationalize many features of the relaxation dynamics of these systems [2], the answers to certain important questions (e.g. the relaxation dynamics at low temperatures) are still unknown. A further popular approach is the phenomenological concept of "cooperativity", introduced by Kauzmann [3], and Adam and Gibbs [4]. A typical example of this cooperativity is the so-called "cage-effect", i.e. the fact that in a dense liquid each particle is surrounded by neighboring particles which form a temporary cage. In order to allow the particle to change its position the cage has to open up. However, each of the particles of the cage is itself also caged and hence can move only if other particles make room. Therefore one can conclude that the particle motion is collective and there exist "cooperatively rearranging regions" (CRR's) within the liquid. The typical size of a CRR is postulated to grow with decreasing temperature, hence "rationalizing" the slowing down of the dynamics [4,5].Experimentally it is difficult to test the concept of the CRR's since usually one does not have direct access to the dynamics of single particles. Therefore many studies have focused on investigating systems in spatial confinement. If CRR's do exist and grow with decreasing temperature the dynamics should differ from the bulk behavior as soon as the size of the CRR's at a given temperature becomes comparable to the system size. Indeed, almost all experiments on glass formers confined to porous host material [6][7][8][9][10][11][12] and supported (or even free standing) films [13][14][15][16][17] do indeed show a relaxation dynamics that differs from the one in the bulk. However, so far it has not been possible to give a conclusive interpretation of