Electron energy loss spectroscopy (EELS), in both transmission (TEELS) and reflection (REELS) geometries, can provide a powerful tool to obtain the complex dielectric constant of a material over a very wide energy range. The procedures used are generally complicated having to deconvolve the experimental spectra from a number of different contributions in order to extract the bulk term which is proportional to Im(-1/<()over tilde>). In this work we have adopted a simplified method to analyse REELS data under the assumption of a weak surface contribution to the plasmon losses due to the large mean free path for inelastic scattering of the investigated samples. The so deduced dielectric constant is presented, up to 50 eV, for some a-CNx, thin films deposited by pulsed laser ablation of graphite targets in a controlled nitrogen atmosphere. The results are compared with the experimental data obtained by conventional optical reflectivity and also with those obtained from pure amorphous carbon.