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Two experiments were conducted to examine the question of whether stimulus classes between stimuli formed at reaching to criterion in a matching-to-sample discrimination had two properties of stimulus equivalence relation in rats: symmetry and transitivity. In Experiment 1, two thirds of the rats were trained to associate both a particular sample (CONV) with one of comparisons (H) and another particular sample (0) with the other comparison (V) to criterion, or were overtrained. Then they were given two backward association tasks. The remaining rats received a pseudo matching-to-sample discrimination training in Phase 1, but were given the same training as the other rats in Phase 2. The rats trained with the matching-to-sample discrimination learned the shift problem faster than the rats trained with the pseudo matching-to-sample discrimination. Overtrained rats learned backward associations faster than nonovertrained ones. In Experiment 2, rats were trained to associate a particular comparison stimulus (C) with either of two sample stimuli (Con or Cr). Then they were trained to associate a new comparison (V) with one of the samples (Con). Rats required to choose the new comparison (V) when sample stimulus (Cr) was presented mastered a subsequent task faster than those required to choose the other comparison (H). These results of two experiments suggest that rats can satisfy criteria of symmetry and transitivity for the demonstration of equivalence relation between stimuli.