A Mond-Weir type dual for a class of nondifferentiable multiobjective programs in which every component of the objective function contains a term involving the square root of a certain positive semidefinite quadratic form, is formulated and various duality results, viz. weak, strong and converse duality theorems are established. Further, a pair of symmetric dual multiobjective programs with such nondifferentiable terms is constructed. Also, under an additional hypothesis, this pair of nondifferentiable multi-objective programs is shown to be self dual.