A traveling hydraulic stepless transmission (“HST”), ensures stopping of a vehicle on a slope under high load conditions, maintains stopping the vehicle on flat ground under low load conditions, and enables smooth starting from a stop. The HST includes a neutral check valve (“NCV”) and an internal damping system (“IDS”). The NCV includes a first orifice that opens a first oil passage to a transaxle case when a pressure in the first oil passage is equal to or less than a predetermined pressure, and that connects the second oil passage to the transaxle case when a pressure in a second oil passage is equal to or less than the predetermined pressure. The IDS includes second orifices that connect a high pressure side of the oil passages to the transaxle case when a discharge rate of the hydraulic pump is equal to or less than a predetermined discharge rate.