Resorting to ultrafast processes to synthesize alloy nanoparticles far from thermodynamic equilibrium is subjected to phase transformations that keep particles at a given temperature for periods of time that are usually long with respect to the process pulse durations. Then, reaching non-equilibrium conditions is not straightforwardly associated with the process, as fast as it can be, but rather to heat transfer mechanisms during phase transformations. This latter aspect is dependent on nanoparticle size. Furthermore, other important phenomena, like chemical ordering, are essential to explain the final structure adopted by an alloy nanoparticle. In this work, a specific attention is paid to suspensions submitted either to electrical discharges or to ultrashort laser excitations. After discussing thermodynamic considerations that give the frame beyond which non-equilibrium alloys form, a description of the heating processes at stake is provided. This leads to maximum temperature reached for particles with nanometric sizes and specific conditions to fulfil practically during the quenching step. The way solidification must be processed in that purpose is discussed next. The example of the Cu-Ag system is finally considered to illustrate the advantage of better controlling processes that are currently used to create homogeneously-alloyed nanoparticles made of immiscible elements, but also to show the actual limitations of these approaches.