Equivalence formation, expansion, and reversal were investigated as a result of arbitrary matching associated with specific reinforcers. Four 4- and 5-year-old normal children were taught identity matching with stimuli, A, B, C, and D, and stimulus-specific reinforcement. Then the children were taught two conditional discriminations AB and BC. All subjects showed formation of the ABC stimulus classes; one subject, however, did not show expansion to ABCD classes. This subject was taught to name the D stimuli, he then demonstrated the expanded class. Next, 2 subjects who showed expanded classes were taught identity matching with the reinforcers reversed for the D stimuli. In tests that followed, their matching responses remained consistent with the original equivalence classes. These subjects were then taught to reverse the names for the D stimuli. As a result, the children reversed the classes. The results suggest that class expansion and subsequent reformation of classes may be facilitated when stimulus within each class controls a common naming response.