Ni-Mn-Ga is interesting as a prototype of a magnetic shape-memory alloy showing large magnetic-field-induced strains. We present here results for the magnetic ordering of Mn-rich Ni-Mn-Ga alloys based on both experiments and theory. Experimental trends for the composition dependence of the magnetization are measured by a vibrating sample magnetometer in magnetic fields of up to several tesla and at low temperatures. The saturation magnetization has a maximum near the stoichiometric composition and it decreases with increasing Mn content. This unexpected behavior is interpreted via first-principles calculations within the density-functional theory. We show that extra Mn atoms are antiferromagnetically aligned to the other moments, which expl...