The increasing interest in graded index dielectric films for complex optical coatings has stimulated a great effort in terms of characterization by optical techniques either during deposition or a posteriori. This paper is concerned essentially with post-characterization by spectroscopic ellipsometry. Instrumental developments and computer facilities now make possible the acquisition of ellipsometric and photometric data at different angles of incidence, over wide spectral range, in different configurations as well as treatment of data by numerical methods. Refractive index profiles are determined for the most part by fitting of experimental data following two approaches : a discrete description in which the inhomogeneous film is divided into a small number of homogeneous sublayers and a continuous description using a model-function for the index (or composition) variation. Upon consideration of two examples, namely, gradients of composition in silicon oxynitride films and refractive index profile in a Ta2O5 film implanted with Ti ions (with film thickness of around 400 nm in both cases), the discrete description appears useful when the shape of the profile is not known, and in all cases it supplies initial values in the fitting procedure for parameters of the model-function.