Abstract: An object is to provide a steering system for a tracklaying vehicle which is capable of preventing overrun of a motor during a pivot turn irrespective of the load of the road surface and does not cause a shortage of power during a turn. The steering system is comprised of a pair of brakes for right and left output shafts and designed to transmit the driving force of a hydraulic motor to the output shafts through a planetary gear mechanism. A transmission of a driving force from the hydraulic motor to the planetary gear mechanism is interrupted after concurrently carrying out actuation of a brake for either one of the right and left output shafts and a transmission of a driving force from the hydraulic motor to the planetary gear mechanism for a specified period of time, when the vehicle carries out a pivot turn. During a pivot turn of the vehicle, the engine is controlled such that a vehicle body speed obtained by a bevel shaft rotational speed detector becomes equal to a specified value.