Two distinct pairs of secound order symmetric dual programs are considered and appropriate duality theorems are established under η1-convexity/η1-concavity and η1-pseudoconvexity η2-psecoudoconcavity of the kernel function K(x,y). Assuming the additional hypothesis of skew symmetry for K(x,y) these programs are shown to be self dual. Also, it is observed that for a particular kernel function, both these pairs are reduced to the general nonlinear problem and its Wolfe type secound order dual introduced by Mangasarian.