The development of a pseudorotaxane motif capable of performing unidirectional threading and dethreading processes under control of external stimuli is particularly important for the construction of processive linear motors based on rotaxanes and, at least in principle, it discloses the possibility to access to rotary motors based on catenanes. Here, we report a strategy to obtain the solvent-controlled unidirectional transit of a molecular axle through a molecular wheel. It is based on the use of appropriately designed molecular components, the essential feature of which is their non-symmetric structure. Specifically they are an axle containing a central electron-acceptor 4,4′-bipyridinium core functionalized with a hexanol chain at one side, and a stilbene unit connected through a C6 chain at the other side, and a heteroditopic tris(phenylureido)-calixarene wheel. In apolar solvents the axle threads into the wheel from its upper rim and with the end carrying the OH group, giving an oriented pseudorotaxane structure. After a stoppering reaction, which replaces the small hydroxy group with a bulky diphenylacetyl moiety, and replacement of the apolar solvent with a polar one, dethreading occurs through the slippage of the stilbene unit from the lower rim of the wheel, that is, in the same direction of the threading process. The essential role played by the stilbene unit to achieve the unidirectional transit of the axle through the wheel, and to tune the dethreading rate by light is also demonstrated.