Abstract: In Hausdorff locally convex spaces, the concept of super saddle points of a setvalued map is introduced by means of Lagrange setvalued map for the setvalued vector optimization problem (SOP). Two scalarization lemmas are proved, and the theorem of super saddle points and the equivalent characterization of super saddle points are obtained by the separation theorem o f convex sets. Therefore the issues charactering super efficiency by super saddle points are solved.

Key words: super saddle point, super efficiency, setvalued map, optimality condition