The quasilinearization technique is applied to a pursuit-evasion game involving an interceptor and a supersonic bomber. Aerodynamic forces and variable density effects are included. A technique for treating the singularity in the linearized differential equations at the final time is described. Means of expanding the region of convergence are described and utilized to obtain good convergence properties in the example treated. The technique is also applied to determine worst case performance of a specified suboptimal intercept strategy. Quantitative measures are thus obtained for the guaranteed performance and the best possible guaranteed performance.