X-ray apparatus comprises a linear accelerator adapted to produce a beam of electrons at one of at least two selectable energies and being controlled to change the selected energy on a periodic basis, and a target to which the beam is directed thereby to produce a beam of x-radiation, the target being non- homogenous and being driven to move periodically in synchrony with the change of the selected energy. In this way, the target can move so that a different part is exposed to the electron beam when different pulses arrive. This enables the appropriate target material to be employed depending on the selected energy. The easiest form of periodic movement for the target is likely to be a rotational movement. The target can be immersed in a coolant fluid such as water. The linear accelerator can be of the type disclosed in WO2006/097697A1. The target preferably contains at least one exposed area of tungsten and/or at least one exposed area of carbon. These can be present as inhomogeneities in the material of which the target is composed, such as Carbon inserts in a Tungsten substrate (or vice versa), alternating segments of Carbon and Tungsten, Carbon and Tungsten inserts in a substrate of a third material, or arrangements involving other materials in addition to or instead of Carbon and/or Tungsten. Alternatively, the target can be of a homogenous material but have inhomogeneities in its thickness to cater for the different electron energies. The same concept can be applied to the filter. A detector can be provided, operating in synchrony with the energy variation. Such an x-ray apparatus can form a part of a radiotherapy apparatus, in which case the first selected energy can be a diagnostic energy and a second selected energy a therapeutic energy.