We measured the incoherent neutron scattering elastic intensity of hydrated copper azurin at different temperatures in a wide momentum transfer q range. The results show a well-defined non-Gaussian q dependence above 180 K. To investigate the nature of the motions underlying this non-Gaussian dependence, we used a Monte Carlo method to interpret the elastic intensity as the superposition of individual non-dynamically equivalent Gaussian contributions. The calculated probability distribution functions corresponding to such a decomposition are analysed as a function of the temperature. The onset of large amplitude Gaussian motions is responsible for the mean square displacements behaviour, which show above 210 K a marked departure from the harmonic temperature dependence. In addition, such an approach allowed us to correlate the elastic intensity q dependence with the boson peak, a characteristic low-frequency anomaly of protein inelastic spectra. (C) 2000 Elsevier Science B.V. All rights reserved.