The nanoscale alloying of metals with bulk miscibility gaps, Ag-Pt and Ag-Rh, has been investigated using pulsed laser ablation of solids in solution (PLASiS). The procedure was in two steps. In the first step, the suspensions of monometallic nanoparticles were prepared by ablation of a metal rod submerged in water. In the second step, the monometallic suspensions were mixed and alloying was induced by re-irradiation. For the Ag-Pt system, a surface plasmon resonance was observed in the monometallic silver suspension. The surface plasmon resonance vanished in re-irradiated Ag-Pt suspensions, indicating alloying. Selected Area Electron Diffraction (SAED) analysis showed that the nanoparticles had a fcc structure with a lattice constant intermediate between that of monometallic Ag and Pt nanoparticles. First principles theoretical investigations of the mixing energy of Ag-Pt clusters confirm that mixing is favored at around ～1 nm. The same procedure used for Ag-Pt was followed for Ag-Rh. In this system where the two metals present miscibility gaps even in the liquid phase, no evidence of alloying was observed. Correspondingly, theoretical investigations found that the mixing energy of Ag-Rh clusters did not favor alloying.