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Recent research has focused on the variables associated with equivalence-equivalence responding, in which participants match pairs of equivalent or nonequivalent stimuli. One such variable is the presence of response competition from nonarbitrary (physical) relational response options. In the current analysis, the experimenters examined the effect of training conditions on the likelihood of equivalence-equivalence responding in the presence of these competing response options. The conditional discrimination training conditions prompting equivalence relations were systematically manipulated across five experiments. The study included the variable reflexivity training, an equivalence test, the type of stimuli used, and the number of training trials. Results revealed that the manipulations gradually increased the percentage of participants responding in accordance with equivalence-equivalence. The implications of these findings are discussed.