Abstract: To test the tightnesses of two valves arranged upstream respectively downstream of each other in a fluid line, the pressure conditions in the line portion between the two valves is measured with both valves being closed. Following a certain time after the closure of the two valves, the pressure in the line portion is measured to determine whether pressure is above or below a predetermined limit pressure to conclude whether the one or the other valve is tight. Following this determination, the passageway is opened across the valve taken to be tight and the line portion is then drained or filled. During a measuring time interval then following, a differential pressure sensing device measures whether and how often the pressure in the line portion reaches or passes the limit pressure.