The paper reviews the state of research of wave processes in hydraulic systems of machines, and their impact on the quality and stability of hydraulic drives. As noted in the works of previous researchers, these phenomena occur in hydraulic systems and adversely affect the quality and stability of their work, significantly reducing reliability. The method of construction of mathematical models is offered. A mathematical model of the hydraulic system with two series-connected hydraulic motors is built, taking into account transients. The Runge-Kutta-Feldberg method with automatic change of the integration step was used to solve this model. The application of this method makes it possible to estimate the amplitude and frequency of the pressure wave in real time for each part of the pipeline. As a result of the analysis of the obtained transients it was concluded that at the length of the pressure line in a group hydraulic drive with 2 series-connected hydraulic motors up to 1.5 m, wave processes do not significantly affect the system and in the mathematical model they can be ignored. With the length of the pressure line from 1.5 m to 9 m, the wave processes in the cavity do not affect the stability of the system, although significantly impair the quality of its work. Hydraulic systems with a pressure line length of more than 9 m are not recommended for implementation, because the wave processes in the cavity lead to vibrations and noise in the hydraulic system and require additional measures to eliminate the impact of this phenomenon.