Human participant performances often show evidence of learning untrained relations when conditional discrimination training between physically dissimilar stimuli is conducted. These emergent relations document equivalence class formation. The current study investigated whether class-specific consequences (i.e. the specific reinforcers used for each potential class during training) also join the equivalence class. Several studies have suggested they do so. However, training in those studies typically included arbitrary matching and identity matching baselines. In the current study, two autistic children were trained on simple discrimination reversals and identity matching with class specific consequences. They were then given arbitrary matching probes. Performances of both children initially showed evidence of class formation on these tests, despite the fact that neither had received training on arbitrary matching. In addition, one of the participants showed evidence of class formation after simple discrimination reversal training alone. These results demonstrate that the reinforcing consequences do in fact become part of the stimulus equivalence class and provide support for the ideas that equivalence (1) arises from reinforcement contingency and (2) is not based upon language skills.