Both parametric and semiparametric stationary-point- and saddle-point-type efficiency conditions are established for a lass of multiobjective fractional programming problems with subdifferentiable and ρ-convex functions. Subsequently, these efficiency criteria are utilized as a basis for constructing a Lagrangian-type and several Wolfe-type parametric and semiparametric duality models and proving appropriate duality theorems. To illustrate the relevance and applicability of these results, several classes of multiobjective fractional optimization problems which can be viewed as special cases of the main problem are briefly discussed. These include problems with arbitrary norms, square roots of positive semidefinite quadratic forms, support functions, infinitely many constraints, continuous max functions, and discrete max functions.