When and how do children develop an understanding of the subjectivity of intentions? Intentions are subjective mental states in many ways. One way concerns their aspectuality: Whether or not a given behavior constitutes an intentional action depends on how, under which aspect, the agent represents it. Oedipus, for example, intended to marry Yocasta, but did not intend to marry his mother (even though in fact, but unbeknownst to him, Yocasta was his mother). In the present study, we investigated the trajectories and determinants of children's developing understanding of (less dramatic forms of) the aspectuality of intentions. In two studies, children aged 3-9 observed an agent who acted intentionally but based on some mis-representation regarding the target of her action. The agent grasped a box that contained A and B while believing that it only contained A but not B. Children were asked about the aspectuality of the agent's intention (in particular, whether she intended to grasp B). When asked to do so spontaneously, children younger than 8 failed (falsely claiming that the agent intended to grasp B). In contrast, in a simplified format in which children were scaffolded through the required inferential chains, children from age 6 succeeded. Children's general capacity for meta-representation appeared to be necessary but not sufficient by itself for understanding the aspectuality of intentions. The present findings suggest that the appreciation of the aspectuality of intentions is part of an advanced theory of mind that develops in much more protracted ways than basic theory of mind.