A lifting apparatus comprises: a base part, a lifting rope, a sheave assembly, a first rotatably mounted sheave, around which the rope passes and from which the rope extends downwardly to a load, a second rotatably mounted sheave and a drive for moving the sheave assembly. The sheave assembly is mounted for pivotal movement relative to the base part about an axis of pivoting spaced from the axis of rotation of the first sheave and coincident with the axis of rotation of the second sheave. During movement of the load relative to the base part, the first sheave is moved by the drive to compensate for that relative movement, the movement of the first sheave being such that the vertical component of the movement of the first sheave relative to the load is less than the vertical component of the movement of the base part relative to the load.