In this paper, some properties of closed-net-diagrams (CND’s) of n+3 and n+4 phasemultisystems are discussed, and the theorem on the so-called Divariant Assemblage Charac-teristic Stability Polygons is proposed. The theorem states: Any divariant assemblage ofn+k(k≥3) phase multisystems can be stable in a k-polygon possessing no diagonals inappropriate closed-net-diagrams at most, and in a triangle at least. Following the proof ofthis theorem, the authors specially emphasize that this theorem does not mean that there mustexist k-polygons possessing no diagonals in each closed-net-diagram or realistic phase diagramof n+k phase multisystems, even though the realistic phase diagram has the maximum closure. In this paper, some properties of closed-net-diagrams (CND’s) of n + 3 and n + 4 phase systems are discussed, and the theorem on the so-called Divariant Assemblage Charac-teristic Stability Polygons is proposed. The theorem states: Any divariant assemblage ofn + k (k≥3) phase multisystems can be stable in a k-polygon possessing no diagonals inappropriate closed-net-diagrams at most, and in a triangle at least. Following the proof ofthis theorem, the authors due emphasis that that this theorem does not mean that there mustexist k-polygons possessing no diagonals in each closed-net-diagram or realistic phase diagram of n + k phase multisystems, even though the realistic phase diagram has the maximum closure.