Young children often perseverate, engaging in previously correct, but no longer appropriate behaviors. One account posits that such perseveration results from the use of stimulus-specific representations of a situation, which are distinct from abstract, generalizable representations that support flexible behavior. Previous findings supported this account, demonstrating that only children who flexibly switch between rules could generalize their behavior to novel stimuli. However, this link between flexibility and generalization might reflect general cognitive abilities, or depend upon similarities across the measures or their temporal order. The current work examined these issues by testing the specificity and generality of this link. In two experiments with 3-year-old children, flexibility was measured in terms of switching between rules in a card-sorting task, while abstraction was measured in terms of selecting which stimulus did not belong in an odd-one-out task. The link between flexibility and abstraction was general across (1) abstraction dimensions similar to or different from those in the card-sorting task and (2) abstraction tasks that preceded or followed the switching task. Good performance on abstraction and flexibility measures did not extend to all cognitive tasks, including an IQ measure, and dissociated from children’s ability to gaze at the correct stimulus in the odd-one-out task, suggesting that the link between flexibility and abstraction is specific to such measures, rather than reflecting general abilities that affect all tasks. We interpret these results in terms of the role that developing prefrontal cortical regions play in processes such as working memory, which can support both flexibility and abstraction.