For some time now we have been occupied with the implications of two-particle exchange. This leaves several important areas unexplored, however. There is the obvious question of extending the procedures to more elaborate multiparticle exchange mechanisms. And the practical applications of the results have been essentially limited to the idealization of a particle moving in a prescribed field, avoiding the relativistic two-body problem. This chapter is concerned with both types of investigations. But, in order to prevent too heavy a concentration of the often ponderous calculations involved in the higher order multiparticle exchange processes, such discussions will be interspersed among the two-body considerations, somewhat as dictated by the relevance to comparison with experiment.