Abstract. The composition dependences of crystal lattice parameters, bulk modulus, magnetic moments, magnetic exchange parameters in Ni2-yCoyMn1.5-xCrxSn0.5 (y = 0.2, 0.4; 0.0 x 0.4) Heusler alloys are investigated with the help of ab initio calculations. Our simulations have shown that crystal lattice parameter firstly increased and then decreased with Cr content (x) increasing. The strongest ferromagnetic interaction for Ni1.6Co0.4Mn1.4Cr0.1Sn0.5 is nearest-neighbor interaction between Co and Mn1 (on own sites). The strongest antiferromagnetic interaction is observed between nearest-neighbor Mn1-Cr atoms in the first coordination sphere and it is equal to -15meV. Total magnetic moment of Ni2-yCoyMn1.5-xCrxSn0.5 (y =0.2, 0.4; 0.0 x 0.4) takes value in region from 6.1 μB to 6.6 μB.