The instantaneous flow state of the scavenging medium in the cutting plant work gap is determined and operating parameters of the spark-erosive cutting process are regulated and/or controlled as a function thereof. These operating parameters include the generator machining parameters such as pulse magnitude, pulse duration and pulse interval; the relative feed rate of the tool electrode; and the supply of the scavenging medium. For this purpose, the cutting plant includes a device for pressure and/or suction scavenging of the work gap and a control device for adaptively controlling the operating parameters, including at least one sensor for determining the instantaneous flow state of the scavenging medium in the work gap and at least one control element.