We applied first-principles total-energy calculations to several compounds Mn 2¹x M x Sb (M = Ti, Cr, Co, or Cu) to calculate the total energy. The results indicate that the Ti and Cu (Cr and Co) atoms prefer the Mn(II) site to the Mn(I) site [Mn(I) to Mn(II)]. These results are consistent with experimental observations. The antiferromagnetism (AF) [ferrimagnetism (FR)] is more stable than FR (AF) upon decreasing (increasing) the distance between the Mn(II) and Sb atoms in the z direction in all Mn 2¹x M x Sb systems. This result indicates that the environment around the Mn atom plays a very important role in the stabilization of the AF state, as is the case with Mn 2 Sb 1¹x As x systems. For Mn 2¹x Co x Sb systems, the atomic disorder between the Mn and Co atoms is insensitive to the relative stability of two magnetic phases AF and FR.