Five experiments assessed associative symmetry in pigeons. In Experiments 1A, 1B and 2, pigeons learned two-alternative symbolic matching with identical sample- and comparison-response requirements and with matching stimuli appearing in all possible locations. Despite controlling for the nature of the functional stimuli and insuring all requisite discriminations, there was little or no evidence for symmetry. By contrast, Experiment 3 demonstrated symmetry in successive (go/no-go) matching, replicating the findings of Frank and Wasserman (2005). In view of these results, I propose that in successive matching, (1) the functional stimuli are stimulus-temporal location compounds, (2) continual nonreinforcement of some sample-comparison combinations juxtaposed with reinforcement of other combinations throughout training facilitates stimulus class formation, (3) classes consist of the elements of the reinforced combinations, and (4) common elements produce class merger. The theory predicts that particular sets of training relations should yield "antisymmetry": Pigeons should respond more to a reversal of the nonreinforced symbolic baseline relations than to a reversal of the reinforced relations. Experiment 4 confirmed this counterintuitive prediction. These results and other theoretical implications support the idea that equivalence relations are a natural consequence of reinforcement contingencies. (Contains 18 figures, 4 tables and 2 footnotes.)