An X-ray source and an X-ray apparatus with an X-ray source are provided, the X-ray source includes a liquid metal target which flows through a system of ducts and is conducted through a duct section which has a flow cross-section that is reduced relative to that of the system of ducts. The X-ray source provides a pressure source for acting on the liquid metal target such that the pressure in the liquid metal target at the area of the reduced flow cross-section equals essentially a selectable reference value or remains essentially in a pressure range between selectable limit values of the pressure. A comparatively small thickness of a window can thus be realized in conjunction with a comparatively high flow speed.