We have carried out an experimental study on the mechanical relaxation of Langmuir films of a glass-forming polymer, poly-(4-hydroxystyrene), a good example of a two-dimensional system made of condensed polymer coils (at poor-solvent conditions). This study allows us to explore the response functions of the film and the temperature and density dependencies of the relaxation time. The dynamical properties show glasslike features (non-Debye mechanical response and non-Arrhenius relaxation times) reconcilable within the frame of the mode-coupling model.