This study tested the theory that advances on theory-of-mind tasks and on executive function tasks show a strong correlation because the typically used theory-of-mind tasks pose the same executive demands. In Experiment 1 with fifty-six 3- to 6-year-old children, performance on the dimensional change card-sorting task as an executive function task was correlated with performance on the usual false-belief prediction task, r = .65, and the false-belief explanation task, r = .65, as measures of theory-of-mind development. Because the explanation version of the false-belief test is supposed to be free of the alleged executive demands inherent in the prediction version, the equally strong correlation with the executive function task suggests that this correlation cannot be due to common executive demands. In Experiment 2, the basic finding of Experiment 1 was replicated on another sample of 73 children, ages 3 to 5.5 years. The need for new theories to explain the developmental link between theory of mind and executive function development is discussed, and some existing candidates are evaluated.