Being the basis of modern electronics, silicon-germanium semiconductor alloys are widely used in a great number of fields. In this paper, the phase equilibria in Si-Ge nanoparticles have been simulated using a thermodynamical approach. Calculations show that nanoparticles of different diameters and compositions have unique sets of nanoscale liquidus and solidus temperatures which differ significantly from the reference data for the bulk alloy, and the range between nanoscale liquidus and nanoscale solidus temperatures narrows with reducing the particle size. Unlike bulk alloys, the compositions of co-existing liquid and solid phases at different temperatures dramatically differ in nanoparticles with various Si contents while the dependences of equilibrium phase compositions and volume fractions of co-existing phases on particle diameters have turned out to be different at various temperatures and atomic fractions of Si in a nanoparticle. A thermo-dynamical interpretation of the obtained results has also been given based on several mechanisms of lowering the free energy of the system.