The preparation of gold-silver nanoparticles with a core-shell structure by radiation chemistry is described. The optical properties of particles containing Au cores and Ag shells are compared to those of the reverse system for a variety of overall particle compositions. Nanosecond and picosecond laser-induced heating (at 532 nm) is used to melt the AU(core)Ag(shell) particles into homogeneous alloyed nanoparticles. The transition from the kinetically stable core-shell structure to the alloy is demonstrated by TEM and by the spectral changes accompanying melting. It is found that the particles must accumulate many laser pulses to completely mix into the alloy. In the case of nanosecond excitation, alloying and reshaping from faceted and irregular particles into smooth spheres occurs at absorbed energies of 5-6 mJ/pulse, and fragmentation takes place at higher energies, >10 mJ/pulse. In the case of 30 ps laser excitation, the thresholds for alloying/reshaping and fragmentation are lower: 1 and 4 ml/pulse, respectively. The higher energy threshold for nanosecond excitation compared to the picosecond case is due to dissipation of the absorbed energy to the solvent during excitation, which is estimated to occur on a 100-200 ps time scale. Thus, the temperatures reached in the particles by nanosecond excitation are lower than those achieved by picosecond excitation for equal pulse energies.