The pursuit-evasion games with two players and one target for an affine nonlinear control system were investigated.The problem of determining the discriminating domain in the region with inequality constraints for this class of control system was solved and a necessary and sufficient condition was given out.Based on viability theory and nonsmooth analysis method,a theorem of determining the discriminating domain for the nonlinear system was obtained,so that the problem can be transformed into the problem of determining the consistency of convex inequalities.Then a projection algorithm for solving the problem was provided based on the algorithm of convex feasible problem.The convergence theorem of the algorithm was received and finally the alternative theorem for pursuit evasion games with two players was achieved.