For the first time a series of ceramic powders of the composition (Y1–xLux)3Yb0.15Er0.03Al5O12 (YLuAG) with a garnet structure in which the atomic ratio of Y3+/Lu3+ cations varied from 80/20 to 20/80, were synthesized using the chemical coprecipitation method. It was determined that the process of garnet phase formation under the synthesis conditions used occurs through the formation of intermediate phases, the composition of which depends on the Y/Lu ratio in the solution of the initial salts. Based on the results of differential thermal analysis of precursor powders and X–ray diffraction of ceramic powders of the composition (Y1–xLux)3Yb0.15Er0.03Al5O12, calcined at 800, 900, 1000 and 1150 ?C, the temperature ranges of formation and decomposition of intermediate crystalline phases Y2O2SO4, Y2(SO4)3, Lu2(SO4)3 and Lu1–xYxAlO3, formed in the process of temperature synthesis of the phase with the garnet structure, were determined.