Abstract: In this paper, a three dimensional pursuit-evasion problemis studied by the differential game theory. The time constants and axial accelerations of the missile and target are taken into account. The steering characterises of the optima] strategy are analyzed in detail. Analyses show that the optimal strategy is actually a feedback control by giving predicted miss as error signal. It is also a modified proportional navigation guidance law. Its ideal motion at each sampling instant is approximately the well-known constant bearing course. Neglecting the time canstants, axial accelerations and the control overflow, the optimal strategy is reduced to the conventional proportional navigation guidance law. The control ability of the flight vehicle to the situation is defined and discussed. Finally, from the computation and analysis of the optimal gain, we get deeper understanding about the optimal strategy. The results obtained will be useful for the guidance system design of the new generation flight vehicles.