The optimal control for an evasive target in a particular pursuit-evasion conflict has been determined. The pursuit vehicle has a fixed gain proportional navigation guidance system in which a pure time delay is present. The mathematical model assumes two-dimensional linearized dynamics. It is found that for fixed control energy, the evasive control depends strongly upon the gain and time delay of the pursuit system. Even in the worst case, however, the evader can significantly increase the miss distance that results from no evasive action. In addition, the results indicate the solution to an associated minimax type problem, viz., the choice of gain for the pursuer so as to minimize the (maximum) miss of the optimal evader. The results indicate that for all cases the optimal gain is approximately equal to the fuel optimal gain against a nonmaneuvering adversary and lower than the value obtained by a no-delay differential game analysis.