The structural, electronic, mechanical and dynamical properties of new members of MAX family (Hf2XY, X = Al, Si, P and Y = B, C, N compounds) with Cr2AlC-type structure have been investigated by first-principles density functional plane-wave pseudopotential calculations within generalized gradient approximation. From calculated cohesive energies, all compounds are energetically stable. And, from calculated elastic constants and phonon dispersion curves, it is shown that all compounds are mechanically stable, while the boron including ones are dynamically unstable except for Hf2PB. At the same time, related mechanical properties such as bulk and shear moduli are calculated. For further mechanical characterization, hardnesses of the compounds are determined theoretically. It is observed from electronic structure calculations including band structure and partial density of states, all stable compounds are metallic. Additionally, bonding nature of the compounds are analyzed by using 3D and 2D electron density maps, Mulliken atomic charges and bond overlap populations. (C) 2015 Elsevier Masson SAS. All rights reserved.