The paper is devoted to a study of the formation of submicron and nanosized cellular crystallization structures on the surface of a high-entropy AlCoCrFeNi alloy irradiated by high current electron beams with the energy density varying from 10 to 30 J / cm2 and a pulse time of 200 μs. The study revealed that the combination of thermal, evaporation-capillary and thermoelectric instabilities induces the formation of submicro- and nanodimensional cellular structures similarly to high-entropy alloys. The proposed dispersion equation was analyzed to detect the conditions for the generation of this instability. The importance of the evaporation process was investigated by finding a solution to the heat problem with phase transformations. The temperature distribution over time calculated at different distances from the surface of the alloy samples demonstrated that the surface temperature is lower than the evaporation temperature for the energy density Es < 30 J / cm2, therefore, the term of evaporation in the dispersion equation was ignored for these values of the energy density. The analysis of the dispersion equation showed that for Es = 30 J / cm2, the wavelength λm with the maximal growth rate of perturbations on the melt surface gains a value in the submicro-and nano-range, provided that the thermoelectric coefficient equals to ~4 –10 V / K, and the pressure of evaporation is ~105 Pa. If we exclude thermoelectric effects, these values λm are observed for the pressure of evaporation ~1011 Pa. The wavelength λm was revealed to decrease according to a power law as the beam energy density increases.