The influences of composition and Mn-Ga/Al disordering on the magnetic and elastic properties of the Ni 2 Mn(Al 1Àx Ga x ) Heusler alloy are investigated by the use of the first-principles exact muffin-tin orbital method in combination with coherent-potential approximation. The transition temperature from the completely disordered B2 phase to the ordered L2 1 phase, estimated by the use of Bragg-Williams-Gorsky approximation, is in excellent agreement with experiments. The site-occupancy in the partially disordered alloy is determined by comparing the free energies of the alloys with different site-occupation configurations. It is found that Mn atoms generally prefer to exchange with Al atoms for the alloy with low degree of disorder and low Ga concentration. With increasing degree of disorder and Ga concentration, Mn may exchange with Ga as well. The total magnetic moment of the completely ordered alloy exhibits a minimum around x = 0.7 due to the competition between the increasing magnetic moments of Mn atoms and the decreasing moments of Ni atoms with increasing x. For the partially disordered alloy, both total and local magnetic moments of Mn and Ni decrease linearly with increasing degree of disorder, and Ga atoms show significant magnetism. The shear moduli C 0 of the alloys are calculated with respect to both x and the degree of disorder. The results show that C 0 decreases with increasing x and degree of disorder. The dependence on composition and on the degree of disorder of the martensitic transition temperatures is discussed in terms of the calculated C 0 .