This paper investigates the possibility of arriving at the mixed-strategy solution of a zero-sum two-person game through an iterative learning process. Learning takes place during repeated play of the game, in which the players have no direct knowledge of the payoff matrix but are allowed to record what happens during play. In this context, all members of a wide class of behaviorally plausible learning mechanisms are shown to be locally unstable for "almost all" zero-sum two-person games with mixed-strategy solutions.