For Husserl, kinaesthetic capability is a key piece of the perception process. By ensuring the junction between the actual and the potential, it allows the exhibition of an object that is always more than what appears. Kinaesthetic capability preserves the transcendence of the object by preventing the phenomenon from being confined to pure actuality. This idea, however, poses significant challenges when one questions the nature of the possibilities that are at stake here. Especially, the perceived seems to enjoy a kind of emancipation from these capabilities as they actually are. How can one justify that the structures of the perceived world are the intentional correlate of the kinaesthetic skills of the subject, if such structures continue to regulate the sense of the appearing objects when those skills are neutralized? We will see that only a genetic perspective, assuming the intrinsically historical character of the subject, provides a satisfactory answer to this question, and that this perspective leads to question the actualist position that Husserl sometimes tends to adopt.