This thesis deals with the optimal mid-course guidance for beyond-visual-range air-to-air missiles(BVR AMMs). For conventional air-to-air missiles using a single rocket motor, the maximum range is quite limited, and the interception performance is severely degraded as the range is increased due to the velocity decay by high drag in the gliding phase. On the other hand, the maximum range and the interception performance of modern air-to-air missiles have been greatly improved by adopting a dual-pulse rocket(DPR) motor and a variable-flow ducted rocket(VFDR) motor for its propulsion system. In this regard, this study deals with the optimal mid-course guidance for BVRAAMs equipped with DPR motors and VFDR motors that can derive their maximal performance. The mid-course guidance problems are formulated to trajectory optimization problems, and efficient trajectory optimization algorithms based on pseudospectral sequential convex programming(PSCP) are presented for each type of missile. In addition, an improved trust-region method that combines a trust-region method and a line search method is utilized to improve the convergence property of the PSCP algorithm. Finally, numerical demonstrations are conducted to verify the performance of the proposed algorithms.