Abstract: The liquid jet cutting apparatus contains a cutter head with a nozzle block and a jet exit opening which communicates with a jet discharge passage. A jet of a pressurized liquid cutting medium is formed in the cutter head and the jet exiting from the jet exit opening passes through the jet discharge passage without contacting the wall thereof. The jet discharge passage communicates through an opening in its wall with a pressure transmission line connecting a gas space formed in the jet discharge passage with a pressure sensor. A transmitter is operatively associated with the pressure sensor and is operated when the pressure in the gas space of the jet discharge passage exceeds or drops below a predetermined pressure threshold value. The transmitter acts upon an actuator or control member of a cut-off device or throughflow regulator which is arranged in the liquid supply line which supplies the pressurized liquid cutting medium to the cutter head.