In situ real-time x-ray diffraction was used to study phase segregation and coarsening of Au-Pt nanoparticles supported on silica powder, and porous alumina membranes. Contrary to the expectations from the bulk phase diagram, silica supported Au-Pt nanoparticles have an alloyed structure that is preserved even after extensive annealing at temperatures as high at 700 degrees C. In stark contrast, alumina supported Au-Pt nanoparticles exhibit a rich phase behaviour that is sensitive to alloy composition and the details of the synthesis process. In particular, low-density as-prepared Au41Pt59 nanoparticles exhibit the signature of incipient phase segregation that develops into full phase separation during annealing at high temperature.