The problem of time-optimal fuselage-reorientation maneuvering of a combat aircraft, with and without thrust-vectoring capability, was analyzed. An accurate mathematical model for the reorientation maneuvers of interest was developed, to ensure practical value of the analysis. In particular, an effective method for smooth fitting of the aerodynamic data was devised. The Minimum Principle from optimal control theory was applied and the optimal control problems of interest cast into a form of numerical multipoint boundary-value problems. These are extremely difficult to solve. To alleviate their treatment, a hybrid approach was adopted. Homotopy ideas were combined with comprehensive analyses of the structure of the dynamical equations and engineering insight into the mechanics of the reorientation motions. The approach successfully yielded a number of extremal solutions for a few typical reorientation maneuvers. The nature and essential characteristics of the extremal motions were understood, as well as their domains of existence. A few parametric studies showed how aircraft design parameters should be tailored to allow for improved maneuverability. / Ph. D.