Non-linear stress-strain curves of various films with thickness of one to four microns were determined from nanoindentation experiments with a Berkovich indenter. The measured load-depth data are analysed using a method based on neural networks. An inverse mapping of depth-dependent dimensionless hardness and stiffness data yields the material parameters describing a non-linear elastic-plastic stress-strain curve of the Armstrong-Frederick type. Suppositions for the application of this method are a sufficiently different hardness between film and substrate, and hardness and stiffness data available in a depth range of 10 to 200% of the film thickness. For all films considered a significant thickness dependence in strength has been observed. In addition, a remarkable influence of the substrate material on the strength of the film material was found and has been confirmed by focussed ion beam microscopy.