Guidance laws are developed for both pursuer and evader satellites, using a simplified dynamic model of the one-on-one satellite encounter. Dynamic symmetry is assumed: both have noisy azimuth-elevation data, the criterion for each is the expected miss, and both satellites have on-off thrust inputs of controllable direction. Sample times and control times are simultaneous, and the known time of minimum range is independent of the controls. Under a set of plausible assumptions, the expected miss is minimized by the pursuer and maximized by the evader. Typical solutions are illustrated, and refinements are discussed. Nomenclature Ap9 Ae = maximum control acceleration levels of pursuer and evader dA,dE = error in azimuth and elevation data die = control time interval dupe, duep = error in estimate by evader and pursuer of each other's control dxp, dxe = error in estimate of vector state by pursuer and evader dyp, dye = difference of data and predicted data of pursuer and evader e = normalized change in miss due to evader's thrust input F = discrete transition matrix (4x4) G =