Part I of the paper was devoted the theory of Φ-conjugation. This theory is used in the present paper for giving optimality conditions of a class of nonconvex programming problems, A geometrical version (founded on supporting hyperplanes and their relation to the polarity of a hypersurface of order two) as well as an analytical version of the optimality conditions are given. New results and also several Well Known optimality conditions for convex programming problems and for general fractional programming problems are presented.