In a method for monitoring and positioning a beam or jet for operating on a workpiece, a first sensor (eg. in the case of a beam, a seam detecting system) ahead of the beam or jet, and/or a preset value, determines the path to be followed by the beam or jet. A second sensor behind the beam or jet monitors the action of the beam or jet. The preset value, or the readings obtained by the first sensor regarding a required position of the beam or jet, is or are compared with readings obtained by the second sensor regarding an actual position of the beam or jet, taking account of the velocity-dependent relative displacement between the beam or jet and the workpiece. The beam or jet is corrected to a basic position if the actual position deviates from the required position.