The joint research of scientists of two countries deals with cylindrical and surface grinding with abrasive wheels of heat-resistant steel Inconel 625 (KhN77TYu GOST 5632 – 72 Russian Federation standard), (analogues include Hastalloy, N07080, Alloy 80A, Nimonic 80A, 2.4952 ASTM B637/ASME SB637, UNS N07080). The article shows the results of studies of the features of high-temperature steel during grinding with a fastened abrasive. The results of experiments are given to determine the optimal characteristics of grinding wheels, grinding modes, cooling-lubricant fluids. Experimental data about geometric accuracy, surface roughness, resistance of wheels are demonstrated as well. The ways to prevent from defects during cylindrical and surface grinding of high-strength steel are proposed. The recommendations to increase the tool resistance and output of the process are given.