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The elastic coefficients and mechanical properties (bulk modulus, shear modulus, Young's modulus and Poisson's ratio) of Ti2Al(CxN1−x) continuous solid solutions for x from 0 to 1 are calculated using ab initio DFT methods on 4×4×1 supercell models. It is shown that the properties of these solid solutions do not vary linearly with x. Although the lattice constant c is almost constant for x≤0.5, a increases linearly. For x>0.5, c starts to increase with x while the rate of increase in a slows down. For x between 0.5 and 0.85, the elastic coefficients and the mechanical parameters show interesting dependence on x and crossovers, signifying the complex interplay in the structure and properties in Ti2Al(CxN1−x) solid solutions. The nonlinear variations in mechanical properties are explained in terms of subtle difference in the electronic structure and bonding between nitrides and carbides in complex MAX phase compounds.