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This study sought to develop methodology for assessing whether children ages 16–21 months could learn to match stimuli on the basis of physical identity in conditional discrimination procedures routinely used in stimulus equivalence research with older participants. The study was conducted in a private room at a day-care center for children and toddlers. Simple discrimination and discrimination-reversal trials were programmed. In the initial training, S+ and S– toys were displayed within 2 windows. When the child touched the window containing the toy defined as S+ on a given trial, she or he was allowed to manipulate/play with that toy. Selections of the S– toy ended the trial without a play opportunity. The study provides evidence that preverbal children can master simple and conditional discrimination performances via such procedures, perhaps setting the stage for subsequent studies needed to assess the stimulus equivalence potential of children in this age range.