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A Mond-Weir type second order dual to a variational problem is constructed and the notion of second order invexity and second order generalized invexity are introduced in variational problems. Under these second order pseudoinvexity and second order quasi-invexity assumptions, weak, strong and converse duality results are established. It is pointed out that our duality results can be considered as dynamic generalizations of corresponding (static) duality results in nonlinear programming.