A pair of symmetric dual nondifferentiable fractional programming problem is formulated in which both the numerator and denominator of the objective function contain a term of the support function of a compact convex set. For this pair, weak and strong duality theorems are established under convexity-concavity of the numerator and concavity — convexity of the denominator. Under additional assumptions, this pair of nondifferentiable problems is shown to be self dual. Special cases involving square root of positive semi-definite quadratic forms are deducible from these results.