Realtime beam shape adjustment in response to (for example) online CT scanning of a patient during treatment is assisted by the radiotherapy apparatus comprising a source adapted to emit a beam of therapeutic radiation, a collimator for delimiting the radiation beam, the collimator comprising a plurality of leaves arranged alongside each other and be moveable longitudinally so that the tips of the leaves define a variable edge of the collimator, the leaves being mounted on a support that is moveable laterally with respect to the leaves. In this way, movements of the tumour that are perpendicular to the direction of leaf motion can be accommodated by simply moving the collimator bodily so as to accommodate this. It is preferred that the apparatus also includes a control means adapted to receive information as to the location of the target volume, and, on the basis of that information, control the longitudinal positions of the leaves and the lateral position of the support. It is also preferred that the support tilts as it moves laterally along a path. This can be achieved, by example, by bearings that are moveable on suitable guides, or by mounting the support on a plurality of pivot arms of unequal lengths. The lengths of such pivot arms can be adjusted as necessary.