Abstract <p>Within the kinetic-atomistic approach, nonequilibrium phase transformations of melting/crystallization of copper and gold, arising under the influence of ultrashort laser radiation, are studied. One of the manifestations of the nonequilibrium of melting/crystallization processes is thermal hysteresis, which is characterized by a mismatch between the melting and crystallization temperatures, as well as the thermodynamic characteristics of the material (enthalpy, density) during heating and cooling. The magnitude of thermal hysteresis, being a characteristic of the degree of overheating/undercooling of the condensed phase, is associated with the velocity of the phase front. The velocity of the melting/crystallization phase front, representing the response function of the interphase boundary to overheating of the solid or undercooling of the liquid phase, is a fundamental quantity describing the processes of crystallization and melting, and plays a fundamental role in materials science. An analytical dependence of the steady-state velocity of the front in the region of maximum permissible values of overheating/undercooling was obtained by comparing the results of atomistic modeling and the data of the kinetic model of the melting/crystallization front mobility using the example of Cu in the crystallographic orientation 〈100〉. The temperature dependence was obtained in the range from the limiting temperature of undercooling of the liquid phase to the limiting temperature of overheating of the solid phase using the least-squares criterion. The accuracy of the constructed function is determined by the proximity to the values of the atomistic modeling data and does not depend on the influence of difficult-to-measure and not always strictly defined thermophysical parameters of the metal, such as the activation energy, the mean free path of atoms in melting/crystallization processes, etc. The range of temperatures of limiting overheating/undercooling for obtaining the temperature dependence of the melting/crystallization front velocity was obtained from the properties of thermal hysteresis. Thermal hysteresis of enthalpy and density of copper and gold was obtained based on the results of atomistic modeling in the temperature range of 600 ≤ <i>T</i> ≤ 2000 K in order to study the nonequilibrium processes during melting/crystallization phase transformations, i.e. during the solid/liquid transition. The melting/crystallization characteristics such as the limiting temperatures of overheating/undercooling, the values of relative overheating/undercooling, the energy costs for nucleation during melting of the solid and crystallization of the liquid phases were obtained, and the regions of metastable states of the solid and liquid phases were determined. The position of the melting/crystallization fronts was tracked using the order parameter. The temperature dependence of the solid/liquid interface velocity for Cu, like all thermal hysteresis characteristics, shows a clear asymmetry with respect to the melting point <i>T</i>_m, which is explained by the strong difference between the melting kinetics in the highly overheated state and the solidification kinetics in the highly undercooled state.</p>