A speed-reducing valve assembly is provided in an air passage through which compressed air is discharged when a pneumatic actuator is decelerated. The speed-reducing valve assembly comprises a three-way valve actuated by a signal generated when the actuator has reached the point where deceleration is started, a relief valve through which the compressed air in the passage is let out when the air pressure has reached the preset level, and a check valve that allows only the admission of compressed air into the same passage. The signal-actuated three-way valve brings the air passage of the actuator into communication with the passage in which the relief valve and check valve are provided. When the signal generated when the actuator has reached the deceleration starting point is fed to the speed-reducing valve assembly, the exhaust passage of the actuator communicates with the relief valve and check valve. If the pressure in the actuator is lower than the desired level, the check valve opens to introduce a fluid of the desired pressure through the pressure-reducing valve. If the inside pressure is higher, the air is discharged through the relief valve. Thus the pressure in the exhaust-side pressure chamber of the actuator is always maintained at the desired level. The piston of the actuator is therefore rapidly and smoothly brought to a stop at the desired point.