The terminal stage of a minimum-time mission of a high- performance aircraft is studied using both a reduced-order "energy" model formulation and a point-mass model formulation of the aircraft. The mission is confined to vertical plane maneuvers, and is defined as consisting of three stages; a climb to the dash point,a steady-state dash at the high velocity point, and finally, a terminal transient from the dash point to the final state. This terminal maneuver evolves outside of the flight envelope, rapidly decreasing altitude while increasing the velocity to values greater than the dash velocity. The velocity then decreases from this maximum value as required in order to meet the final state specification. Some of the trajectories that are generated during this terminal transient maneuver experience dynamic pressures that will exceed the dynamic pressure limit unless a constraint is placed on the state variables. Because of the need for enforcing this state constraint, a direct adjoining method for handling state constraints in the optimal control problem is studied. A numerical example is given to demonstrate the application of this method of handling state constraints for the case of the dynamic pressure limit. Finally, trajectories are generated that lead from the dash point to a final state having lower altitude and energy values than those of the dash point, and observations are made concerning the characteristics of these maneuvers. / Master of Science