Alloy nanoclusters ("nanoalloys") are of interest because of their novel properties compared to bulk alloys. In this paper, the thermal behavior, including melting, of 55 atom Ag-Au nanoalloys has been investigated by molecular dynamics simulations using the Gupta many-body potential. Single melting runs exhibit a sharp transition from the cluster ground structures to the melt, while averaged results indicate that melting occurs in a size- and composition-dependent temperature range. The transition point (melting point) decreases with increasing Au concentration. Gold-rich AunAg55-n nanoalloys with n = 30-55 exhibit a very smooth transition from the ground state to their undercooled melt. Their thermal stability is influenced by the glass transition behavior of the pure amorphous Au-55 cluster.