Abstract:The concept of second order radial epiderivatives for set valued mappings was introduced into the real normed space, and then some results which are found true within the concept of the first order radial epiderivatives were extended to the second order radial epiderivatives, thus to obtain five necessary and sufficient optimality conditions for efficient points in the real normed spaces. This kind of concept of second order radial epiderivatives for set valued mappings can simplify optimality conditions and help achieve unity between the necessity and sufficient optimality conditions, which makes it possible for such a concept to find application in various kinds of efficient solutions for set valued optimization problems.