We present the results of measurements of the dynamics of polymer molecules confined to thin freely-standing films on two different length scales: measurements of the glass transition temperature 'T g' which provided a measure of mobility on the segmental length scale, and measurements of the growth of holes which probed the mobility of entire chains. Since the time scale for motions on different length scales are found to have the same temperature dependence in bulk systems, it is of interest to question whether or not motions on these two length scales would be equally increased in thin polymer films. Previous measurements of freely-standing polystyrene (PS) films using Brillouin light scattering and ellipsometry have shown large (up to 70°C) reductions in 'Tg' for very thin films. Measurements performed on freely-standing films of another polymer, poly(methyl methacrylate) (PMMA), using ellipsometry are presented in this thesis and show qualitatively similar reductions in 'Tg' with decreasing ' h', but with a much smaller magnitude of the reduction (only a 20°C reduction for 'h' = 30 nm). These observed 'Tg ' reductions indicate substantial increases in mobility on the segmental length scale. The motion of polymers on the length scale of the entire chain was studied by measuring hole growth in freely-standing PS films. Optical microscopy provided a direct measure of the radius as a function of time, 'R'(' t'), of a single hole in the film, while a custom-built differential pressure experiment (DPE) determined the growth time [tau] of the holes by measuring the flow of gas through the all holes present in the freely-standing film as a function of time. The 'R'('t') behaviour in these PS films at temperatures close to the bulk value of the glass transition temperature T^bulkg were found to be well described by an expression for exponential hole growth with a time-dependent viscosity eta that allowed for an initial, transient response due to the decay of entanglements. Using the DPE, hole growth measurements were performed on thin films with reduced ' Tg' values, as well as thicker films with the bulk value of 'Tg'. In all the films measured, substantial mobility of the polymer chains, such that holes formed in the films, was only observed at temperatures comparable to T^bulkg . Thus the results of this thesis demonstrate that motions on the length scale of the entire chain are not enhanced in conjunction with the observed ' Tg' reductions indicating a discrepancy between segmental and whole chain motions for thin freely-standing polymer films not observed in bulk systems.