Nanoalloys are often grown or synthesized in non-equilibrium configurations whose further evolution towards equilibrium can take place through complex pathways. In this work, we consider bimetallic systems with tendency towards intermixing, namely AgAu, PtPd and AuCu. We analyze their evolution starting from non-equilibrium initial configurations, such as phase-separated core@shell ones, by means of molecular dynamics (MD) simulations. These systems present some differences, since AuCu bulk alloys make ordered phases at low temperature whereas AgAu and PtPd remain in solid solution. Moreover, Cu, Au and Ag have similar cohesive energies whereas Pt is much more cohesive than Pd. We consider both truncated octahedral and icosahedral initial shapes in the size range between 2 and 3 nm. For each AB system, we consider both A@B and B@A core@shell starting configurations. The evolution is characterized by monitoring the time-dependent degree of intermixing and the evolution of the shape. The simulations are performed up to temperatures close to the melting range. The approach to thermodynamic equilibrium is monitored by MD simulations and compared with the equilibrium chemical configurations obtained by Monte Carlo simulations.