A formal statement of a relational principle of reinforcement is developed that makes contact with analyses of choice, interresponse-time distributions, and stimulus control. Some implications for current theoretical and empirical work in the various areas are examined. In this paper, the relational principle of reinforcement proposed by Premack (1959, 1965) is given a somewhat more formal statement that more explicitly acknowledges the role of the stimulus. This formalization of the reinforcement principle is shown to be consistent with the theoretical analysis of a number of diverse phenomena-including choice behavior , interresponse-time distributions, and the blocking of stimulus control. Relational Principle of Reinforcement Consider the following specific illustration of operant conditioning as a means of introducing the necessary terminology: a pigeon is deprived of food and is placed in an experimental chamber containing a response key and a food hopper, from which mixed grain may be made available. In the presence of the stimulus of the key, the key-pecking response may freely occur in the absence of any contingency imposed by the experimenter. The stimulus of the key is referred to as the noncontingent stimulus (SN) and the response of key pecking as the noncontingent response (RN). Conditioning is instituted when the stimulus of the grain, which stimulus controls pecking, is made contingent on a key-pecking response. The stimulus of the grain is termed the contingent stimulus (Sc) and pecking the grain is termed the 'Preparation of this paper was supported by a grant from the U.S. Public Health Service, MH-17395. For their comments on an earlier version of the manuscript, appreciation is expressed to John contingent response (Rc). When the contingency between key pecking and the stimuli controlling eating is instituted, the frequency of key pecking is observed to increase and the key-pecking response may be said to have been reinforced. According to Premack, a general statement of the events critical to the occurrence of reinforcement is as follows: in the presence of non-contingent stimuli (SN), a noncontingent response (RN) increases in probability if RN is followed by more preferred contingent stimuli (Sc) which control a second response (Rc) and if the organism has been deprived of the contingent response (Premack, 1965). Note that within the context of Premack's formulation, reinforcement is not a property of either a stimulus or a response but of a relationship between two successive elicitation processes, i.e., SN-RN and Sc-Rc (cf. Catania, 1971; Morse and Kelleher, in press). The preference for an elicitation process is defined as the proportion of time that an organism exposes itself to the stimuli that control the response when given free access to the controlling stimuli under baseline conditions which are otherwise identical to the conditions prevailing when the contingency is present. The preference for an elici-tation process is most conveniently measured by the probability (pi) of the response controlled by the eliciting stimulus, and may be defined as m(t1) n > m(t,) 1=1 (1) where m is an appropriate measure of the time, (ti) spent engaging in Ri when there are 341 1977, 27., 341-350 NUMBER 2 (MARCH)