This article and the preceding Part 1 (Anger, 1987) present a new molecular analysis of operant reinforcement and extinction. It is a multifactor analysis of the basic extinction processes that can be studied with procedures that minimize competing behavior. Part 1 showed that response-specific inhibition (RSI; Anger, 1983) can account for animal sensitivity to complex response contingencies. RSI depends on the same events that determine whether a reinforcer is contingent on a response. RSI can average those event frequencies, combine them into a single variable that varies with the contingency, and adjust responding appropriately. In Part 2, the findings of Part 1 were used to derive a rational equation that describes operant responding. That linear additive equation specifies a balance between RSI-augmenting events (e.g., unreinforced responses) and RSI-decrementing events (e.g., reinforced responses). The equation predicts a different relation between responding and reinforcer frequency than do other theories, because it predicts that responding is augmented by an unrecognized variable, unreinforced nonresponse-time during controlling stimuli. 55 This article continues the analysis of Part 1 (Anger, 1987), whose prior reading will probably be needed, although major abbreviations are restated here. The term P represents a response, and P' represents the absence of that response during the stimulus in whose presence P is sometimes reinforced, hereafter called S+.