The article considers the possibility of using mathematical methods to predict thermodynamic processes in single-crystal nickel-based alloys. The task was to obtain regression models to determine the separation of phases in the system. The work used the CALPHAD thermodynamic modeling method, with the help of which mathematical models were obtained, as well as a REM-106I scanning electron microscope with X-ray spectral microanalysis. Theoretical modeling of thermodynamic processes of phase transformations, as well as a practical study of the structure and distribution of chemical elements, were carried out. Based on an integrated approach for the Ni-Al-Re-Cr-Co-W-Mo-Ti-Ta-Nb single-crystal system, new regression models were obtained that allow predicting the chemical composition of the phases based on the chemical composition of the alloy. It was found that when titanium and rhenium exceed 3 and 6%, respectively, TCP phases are formed in the alloy, which reduces the strength of the material. A comparative assessment of the calculation results obtained using regression models and experimental data obtained by X-ray spectroscopy on an industrial alloy after heat treatment was carried out. The experimental results obtained are as close as possible to the calculated data. Thus, it is recommended to use the obtained regression models to predict the phase composition and properties of alloys of this system.