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Structural, electronic, and magnetic properties of Mn₂Co_1-xV_xZ (Z = Ga, Al, x = 0, 0.25, 0.5, 0.75, 1) Heusler alloys were theoretically investigated for the case of <i>L</i>2₁ (space group <i>Fm</i><inline-formula><math display="inline"><semantics><mover accent="true"><mn>3</mn><mo>¯</mo></mover></semantics></math></inline-formula><i>m</i>), <i>L2</i>_1b (<i>L2</i>₁ structure with partial disordering between Co and Mn atoms) and XA (space group <i>F</i><inline-formula><math display="inline"><semantics><mover accent="true"><mn>4</mn><mo>¯</mo></mover></semantics></math></inline-formula>3<i>m</i>) structures. It was found that the XA structure is more stable at low V concentrations, while the <i>L</i>2₁ structure is energetically favorable at high V concentrations. A transition from <i>L</i>2₁ to XA ordering occurs near x = 0.5, which qualitatively agrees with the experimental results. Comparison of the energies of the <i>L2</i>_1b and XA structures leads to the fact that the phase transition between these structures occurs at x = 0.25, which is in excellent agreement with the experimental data. The lattice parameters linearly change as x grows. For the <i>L</i>2₁ structure, a slight decrease in the lattice constant <i>a</i> was observed, while for the XA structure, an increase in <i>a</i> was found. The experimentally observed nonlinear behavior of the lattice parameters with a change in the V content is most likely a manifestation of the presence of a mixture of phases. Almost complete compensation of the magnetic moment was achieved for the Mn₂Co_1-xV_xZ alloy (Z = Ga, Al) at x = 0.5 for XA ordering. In the case of the <i>L</i>2₁ ordering, it is necessary to consider a partial disorder of atoms in the Mn and Co sublattices in order to achieve compensation of the magnetic moment.