For diagnosing car braking systems, bench methods have become the most widespread, and on power stands with running drums. The main disadvantage of these methods is the high cost of brake stands with low quality diagnostic information. At the same time the method of diagnosing brake systems on change of angular speed of the hung up wheels is perspective. But the considered method does not have a sufficiently complete theoretical justification, especially for cars with hydraulic brakes and therefore requires research. Therefore, the work substantiates the diagnostic modes and diagnostic parameters, obtained analytical dependences of the process of braking car wheels with hydraulic brakes, which describe the change in the angular deceleration of the suspended wheels over time in different parts of the brake diagram and the delay time of the brake system. The mathematical model is based on the differential equation of motion of the braked wheel when braking a car with a connected transmission (with clutch engaged) on a straight horizontal section of road. The change in braking torque during braking is determined by the nature of the pressure change in the drive. When braking the wheel, the braking force acts on the radius of the brake drum. The obtained analytical dependences make it possible to study the influence of various factors of the technical condition of brake systems on the performance of the braking process. In order to substantiate the diagnostic modes and diagnostic parameters, analytical dependences of the process of braking car wheels with hydraulic brakes have been developed, describing the change of angular deceleration of suspended wheels in time at different parts of the brake diagram and time delay of the brake system. The obtained analytical dependences make it possible to study the influence of various factors of the technical condition of brake systems on the performance of the braking process.