Identity and oddity matching tasks were designed for different groups of 5-yr.-old children. The presentation of tasks continued until all children had shown evidence of appropriate generalization to new stimuli (i.e., generalized identity matching or generalized oddity from sample). All children then received training on an arbitrary matching-to-sample task. Finally, tests of reflexivity and symmetry in responding were carried out in three consecutive sessions. The children in the Identity group showed reflexivity and symmetry in responses on all three tests; the children in the Oddity group showed oddity in responses on all tests, and a gradual increase in symmetry of responses across tests. These results provide evidence against special versions of multiple-exemplar and reinforcement contingency accounts of stimulus equivalence. Versions of the accounts to explain the findings are discussed.