A radiotherapy apparatus comprises a rotatable gantry, supporting a source of therapeutic radiation and a source of diagnostic radiation, the two sources being rotationally (or angularly) spaced apart around a rotation axis of the gantry, with at least one collimator associated with the source of therapeutic radiation and arranged to limit the cross-sectional area of a beam produced by that source, a control means arranged to conduct a treatment fraction using the apparatus by causing the apparatus to i. acquire images of a patient using the source of diagnostic radiation, ii. retain those images at least temporarily, iii. subsequently, after further rotation of the gantry, select a retained image acquired when the source of diagnostic radiation was at a rotational position corresponding to the instantaneous rotational position of the source of therapeutic radiation, and iv. control the beam relative to the patient using information derived from the selected image. The corresponding rotational position is ideally one in which the source of therapeutic radiation is at the same or substantially the same rotational position as was the source of diagnostic radiation at the point in time when the image was acquired. An alternative a radiotherapy apparatus comprises a rotatable gantry supporting a source of therapeutic radiation and a source of diagnostic radiation, at least one collimator associated with the source of therapeutic radiation and arranged to limit the cross-sectional area of a beam produced by that source, a reconstruction means arranged to i. obtain two-dimensional images of a patient using the source of diagnostic radiation, ii. retain those images at least temporarily, iii. apply a recency threshold to the retained images thereby to exclude images less recent than the threshold, iv. select at least three such retained images meeting the recency threshold and reconstruct a CT volume or tomographic image using the selected images, and a control means arran
