The process of growing crystals of the Ni-Fe-Ga-Co alloy by the Stepanov method has been developed. It was found that the structural perfection is disturbed by the formation of dendrites, which are distributed inhomogeneously both along the length and in the cross sections of the crystals. The blocking effect on the dendrites of crystals of the martensite phase, which appears when the samples are cooled to the temperature of the transition of the crystal to the martensite state, is found. The elemental composition of dendritic formations was studied and it was shown that the iron content in the dendrite is approximately 30% higher, and the gallium content is 40% lower than in the matrix. Based on the modeling of heat transfer processes in the real growth zone, taking into account the experiments performed, recommendations were obtained for suppressing the formation of dendrites