The room temperature changes of the magnetic behavior under pressure of an invar alloy of nominal composition (Fe0.5Cu0.5)87Zr13 (at. %) has been studied by K-edge x-ray magnetic circular dichroism (XMCD) and x-ray absorption near edge spectroscopy (XANES). The Curie temperature, as determined from low field magnetization measurements, is (255 ± 15)K. However XMCD shows a non negligible signal above this temperature. In addition, the XMCD signal decreases upon increasing pressure indicating a pressure-induced collapse of the magnetic moment. These results evidence the itinerant character of FeCuZr alloys as well as the occurrence of magnetovolume effects characterized by a strong dependence of the 3d band on the Fe-Fe nearest neighbor distances.