To evaluate the claim that correct performance on unexpected transfer false-belief tasks specifically involves mental-state understanding, two experiments were carried out with children with autism, intellectual disabilities, and typical development. In both experiments, children were given a standard unexpected transfer false-belief task and a mental-state-free, mechanical analogue task in which participants had to predict the destination of a train based on true or false signal information. In both experiments, performance on the mechanical task was found to correlate with that on the false-belief task for all groups of children. Logistic regression showed that performance on the mechanical analogue significantly predicted performance on the false-belief task even after accounting for the effects of verbal mental age. The findings are discussed in relation to possible common mechanisms underlying correct performance on the two tasks. (Contains 1 figure, 4 tables and 1 footnote.)