A hydraulic static transmission system for use in traveling of a vehicle, the hydraulic static transmission system comprising: a variable displacement motor that drives traveling means; a motor regulator that changes a displacement of the motor; a variable displacement pump connected to the motor such that a closed loop is formed, the variable displacement pump being driven by an engine; a pump regulator that changes a displacement of the pump; a depression amount detector that detects a depression amount of an accelerator pedal; a vehicle speed detector that detects a vehicle speed of the vehicle; a rotation number detector that detects a number of rotations of the engine per unit time; and a controller that controls the motor regulator and the pump regulator, characterized in that the controller: determines whether or not a particular downhill travel condition is satisfied based on a result of detection by the vehicle speed detector and a result of detection by the rotation number detector; and in a case where the depression amount of the accelerator pedal, which is detected by the depression amount detector, is zero and the particular downhill travel condition is satisfied, controls the motor regulator to increase the displacement of the motor; wherein the particular downhill travel condition includes: a condition that the vehicle speed detected by the vehicle speed detector is higher than a setting value; a condition that a derivative value of the vehicle speed is greater than zero; and a condition that the number of rotations of the engine, which is detected by the rotation number detector, is greater than a setting value; and in that the controller controls a fuel injection valve of the engine, and the controller: in a case where the depression amount of the accelerator pedal, which is detected by the depression amount detector, is zero and the particular downhill travel condition is satisfied, controls the fuel injection valve to stop fuel injection into the engine; and in a case where the particular downhill travel condition is still satisfied after the fuel injection into the engine is stopped, controls the motor regulator to increase the displacement of the motor. a variable displacement motor that drives traveling means; a motor regulator that changes a displacement of the motor; a variable displacement pump connected to the motor such that a closed loop is formed, the variable displacement pump being driven by an engine; a pump regulator that changes a displacement of the pump; a depression amount detector that detects a depression amount of an accelerator pedal; a vehicle speed detector that detects a vehicle speed of the vehicle; a rotation number detector that detects a number of rotations of the engine per unit time; and a controller that controls the motor regulator and the pump regulator, characterized in that the controller: determines whether or not a particular downhill travel condition is satisfied based on a result of detection by the vehicle speed detector and a result of detection by the rotation number detector; and in a case where the depression amount of the accelerator pedal, which is detected by the depression amount detector, is zero and the particular downhill travel condition is satisfied, controls the motor regulator to increase the displacement of the motor; determines whether or not a particular downhill travel condition is satisfied based on a result of detection by the vehicle speed detector and a result of detection by the rotation number detector; and in a case where the depression amount of the accelerator pedal, which is detected by the depression amount detector, is zero and the particular downhill travel condition is satisfied, controls the motor regulator to increase the displacement of the motor; wherein the particular downhill travel condition includes: a condition that the vehicle speed detected by the vehicle speed detector is higher than a setting value; a condition that a derivative value of the vehicle speed is greater than zero; and a condition that the number of rotations of the engine, which is detected by the rotation number detector, is greater than a setting value; and in that a condition that the vehicle speed detected by the vehicle speed detector is higher than a setting value; a condition that a derivative value of the vehicle speed is greater than zero; and a condition that the number of rotations of the engine, which is detected by the rotation number detector, is greater than a setting value; and in that the controller controls a fuel injection valve of the engine, and the controller: in a case where the depression amount of the accelerator pedal, which is detected by the depression amount detector, is zero and the particular downhill travel condition is satisfied, controls the fuel injection valve to stop fuel injection into the engine; and in a case where the particular downhill travel condition is still satisfied after the fuel injection into the engine is stopped, controls the motor regulator to increase the displacement of the motor. in a case where the depression amount of the accelerator pedal, which is detected by the depression amount detector, is zero and the particular downhill travel condition is satisfied, controls the fuel injection valve to stop fuel injection into the engine; and in a case where the particular downhill travel condition is still satisfied after the fuel injection into the engine is stopped, controls the motor regulator to increase the displacement of the motor.