The dispersion relations of plasmon-polariton modes in quantised thin but finite semiconductor films are derived and their characteristics features are discussed. It is shown that the lowest two-dimensional unretarded plasma frequency increases strongly with decreasing film thickness in the presence of image charge forces. The dispersion relations are calculated and illustrated for GaAs and PbTe films. Calculations of the nonradiative dispersion spectra indicate that both the transverse magnetic (p-polarised) and transverse electric (s-polarised) plasmon-polariton dispersion spectra possess some gaps. The value of the gap depends on the thickness of the film and carrier surface concentration. It is found that, in thin but finite films, guided and surface localised polariton transverse magnetic modes coincide. For transverse electric modes the coupling between external electromagnetic fields and carriers is weak and almost insignificant.