A lifting apparatus for use in offshore lifting or lowering of a load, the lifting apparatus incorporating a heave compensation arrangement and comprising: a base part; a lifting rope extending from the base part for bearing at least some of the weight of the load; a sheave assembly mounted for pivotal movement about a fixed axis relative to the base part; a first sheave which is rotatably mounted and rotatable about a first axis of rotation on the sheave assembly, around which, in use, the rope passes and from which, in use, the rope extends downwardly for connection to a load; a second sheave which is rotatably mounted about an axis of rotation parallel to the first axis of rotation of the first sheave; the sheave assembly being mounted for pivotal movement relative to the base part of the lifting apparatus 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, the relative movement resulting in movement of the axis of rotation of the first sheave relative to the base part in a direction having at least a major component that is vertical; a drive for moving the sheave assembly; and the apparatus being arranged such that in use during movement of the load relative to the base part of the lifting apparatus, 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 of the lifting apparatus relative to the load characterised in that the first sheave is rotatable about a second axis of rotation, wherein the second axis of rotation is orthogonal to the first axis of rotation. a base part; a lifting rope extending from the base part for bearing at least some of the weight of the load; a sheave assembly mounted for pivotal movement about a fixed axis relative to the base part; a first sheave which is rotatably mounted and rotatable about a first axis of rotation on the sheave assembly, around which, in use, the rope passes and from which, in use, the rope extends downwardly for connection to a load; a second sheave which is rotatably mounted about an axis of rotation parallel to the first axis of rotation of the first sheave; the sheave assembly being mounted for pivotal movement relative to the base part of the lifting apparatus 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, the relative movement resulting in movement of the axis of rotation of the first sheave relative to the base part in a direction having at least a major component that is vertical; a drive for moving the sheave assembly; and the apparatus being arranged such that in use during movement of the load relative to the base part of the lifting apparatus, 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 of the lifting apparatus relative to the load characterised in that the first sheave is rotatable about a second axis of rotation, wherein the second axis of rotation is orthogonal to the first axis of rotation.