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New solutions for actual problems of determination the efficient distribution of braking forces between the axles of the vehicle, and the stability and drivability of two-axles vehicles at service braking are received in the thesis. It permitted for the first time to determine the Law of distribution of the braking forces between the axles, that ensuring straight-running stability of two-axle vehicle at service braking, to obtain the ideal characteristics for the braking system of two-axle vehicle at service braking and to determine possible values for the distribution of braking force on the front axle. The drivability criterion at service braking obtained further development; it is offered to use boundary at gripping front or rear wheels angular vehicle acceleration on the road.