A rare type of nonvariant points on phase equilibrium diagrams occurring only in systems with a large number of components n ≥ 3 (for meltability diagrams) and n ≥ 4 (for solubility diagrams) is considered. It is shown that a melt (solution) does not participate in phase processes occurring at such nonvariant points when heat is removed (solvent evaporated). The stability of monovariant equilibria in the vicinity of such points is studied. The form of fields (volumes, hypervolumes) of crystallization of one of the phases is then peculiar: this is a curvilinear triangle (curvilinear pyramid) resting on a side (face) of the concentration simplex. The figurative points of the compositions of the solid phases coexisting at nonvariant points lie on this side (face) of the concentration simplex.