Glass transition behavior of nanoscopically thin polymer films is investigated by means of molecular dynamics simulations. We study thin polymer films composed of bead-spring model chains and supported on an idealized fcc lattice substrate surface. The impact on the glass transition temperature of the strength of polymer-surface interaction and of chain grafting to the surface is investigated. Three different methods-volumetric, energetic, and dynamic-are used to determine the glass transition temperature of the films. On the basis of these, we are able to identify two different transition temperatures. When the temperature is lowered, a first transition occurs that is characterized by an anomaly in the heat capacity. Upon decreasing the temperature further, a point is reached at which the internal relaxation times diverge, as calculated, using for instance, the mode coupling theory. In qualitative agreement with the experiments, the former temperature depends on the characteristics of the polymer-surface interaction. By contrast, the latter temperature is independent of these.