A multistage vacuum pump unit can save a power requirement and prevent the gas discharged outside of the unit from flowing-back inside the pump unit. A plurality of vacuum pumps are connected in series to form the multistage vacuum pump unit. A suction inlet of a first stage vacuum pump thereof is connected to a to-be-vacuumized container so that the space inside of the container becomes under a high vacuum condition. In an operating method, part of the gas discharged into a first intermediate passage from the first stage vacuum pump is branched during a low vacuum operation, and discharged toward an air atmosphere through a low conductance line provided with check valves that prevent the branched gas from flowing back.