A modified thermodynamic approach to describe melting in isolated nanoscale materials is suggested. The Gibbs free energy change of nanoscale alloy particles is modeled as a function of composition, temperature and nucleus and particle sizes. Cu-Ni has been chosen as a model system due to the availability of thermodynamic data within the high-temperature interval 1300-1600 K. For the first time, "melting loops" in the temperature-composition phase diagram were calculated for nanoparticle of 25 and 80 nm, respectively. It is shown that such loops represent the equilibrium two-phase solid-liquid states and do not coincide with the limiting solubility curves-the solidus and the liquidus. This new finding leads to the "melting loop" concept concerning phase diagrams of nanoscale alloys introduced in this paper. It is found that Cu-Ni nanoparticles can melt in different ways, whereas the dominant transition mechanism is surface-induced melting that initiates from the surface and then proceeds toward the core region. The decrease in size causes also a change of the melting temperature, the temperature width of the phase transition, the solubility limit, the concentration width of the melting loop as well as a change of the shape and slope of the equilibrium curves of the two-phase region of the phase diagram. As expected, when the size of the nanoscale particle increases, the solidus temperature increases and the size-dependent phase diagram approaches the bulk phase diagram.