The first-principles study of the structural,elastic and electronic properties of the M2XC phases depending on the type of M transition metal (M are Ti and Cr) and on X (X are Ga and Al) was reported.The calculations are performed using the pseudo-potential plane-wave approach in both the local density and generalized gradient approximations.The elastic constants are calculated using the static finite strain technique. Features such as structural and elastic parameters,Debye temperature,sound velocities and their pressure dependence have been investigated.In agreement with experimental and previous theoretical findings,it is found that the compressibility along a and c axis depends on the valence electron concentration (VEC).Correlations revealing the governing role of the X and M elements on the machinability indices of the material have been examined.The electronic properties have been discussed in terms of chemical bonding showing that bonding is due to Md-Cp and Md-Xp hybridizations.M-C bonds are stiffer than M-X ones and Al-Ti (Cr-C) bonds are stiffer than those corresponding to Ti-C (Al-Cr).It is shown that the stiffness of the M-X and M-C bonds increases with increasing the number of VEC.