Empirical applications of goal programming with pre-emption to-date have failed to deal with the effects of changes in parameters after the optimal solution has been obtained. A few studies that attempted to do this employed the existing linear programming packages as the basic tool for the analysis, with numerical weights assigned in place of the pre-emptive priority factors. Here an attempt is made to extend the duality theory of linear programming and to relate it to the analysis c f po8t-optimality, especially regarding changes in the priority structure. To this end, the dual problem is constructed and interpreted. It is shown that a duality-based sensitivity analysis helps a decision maker have a better feel for the soundness of bis priority structure of goals.