AbstractThe classification of galaxy clusters according to their X-ray appearance is a powerful tool to discriminate between regular clusters (associated to relaxed objects) and disturbed ones (linked to dynamically active systems). The compilation of the two subsamples is a necessary step both for cosmological studies- oriented towards spherical and virialized systems- and for astrophysical investigations - focused on phenomena typically present in highly disturbed galaxy clusters such as turbulence, particle re-acceleration, magneto-astrophysics.In this paper, we review several morphological parameters: asymmetry and fluctuation of the X-ray surface brightness, hardness ratios, X-ray surface-brightness concentration, centroid shift, and third-order power ratio. We test them against 60 Chandra-like images obtained from hydrodynamical simulations through the X-ray Map Simulator and visually classified as regular and disturbed.The best performances are registered when the parameters are computed using the ...