IF drugs b and c are competitive antagonists of drug a, then it would seem self evident that the addition of c to a system in which b was already present would increase the degree of block. But where the receptors are exposed to the agonist for only a short time there is another possibility. If the first antagonist dissociates from the receptors slowly, and the second rapidly, the additional presence of the second antagonist may increase the number of receptors effectively available to the agonist. If, for simplicity, it is supposed that equilibrium between receptors and both the agonist and the “fast” antagonist is instantaneous and that the dissociation rate of the “slow” antagonist is so small that no dissociation occurs during the period of exposure to the agonist, then it is easily shown that the action of the fast antagonist can be described by the relation where ybc is the fraction of receptors occupied by the agonist in the presence of both slow (b) and fast (c) antagonists, yb the fraction occupied by the agonist in the presence of only b, X is the fraction of receptors which would have been occupied by c, Y by the agonist and Z by b at equilibrium if each of the substances had been present alone. Evidently, if ybc/yb is greater than 1, the addition of the fast antagonist will be expected to increase the response to a standard dose of agonist. Fig. 1 shows how ybc/yb varies with X and Z for two different values of Y. For the larger value of Y the paradoxical effect is observed for a range of values of X and Z; for the smaller value of Y, only additional block is seen. In general, ybc/yb cannot be greater than 1 if Y+Z < 1.