Method for detecting defects in a non-linear weld seam or a non-linear cutting gap during a machining process using a laser beam which is moved along a predefined non-linear welding or cutting path over the workpieces to be machined in order to generate the weld seam or the cutting gap by means of a machining head, comprising the steps of: a) detecting, in a two-dimensionally spatially resolved manner, radiation (70, 70', 82, 82') emitted and/or reflected by the workpiece by means of a detector which is arranged in or on the machining head, characterized by the following steps: b) selecting at least one detection field section (60, 68, 68', 78) in changing positions in the detection field of the detector - on the basis of control data for controlling a movement of the laser beam along the predefined cutting or welding path or - on the basis of previously determined actual-position data of the laser beam along the welding or cutting path, wherein the actual-position data of the laser beam are determined on the basis of position coordinates of a deflector means arranged in the machining head about its pivot axes, wherein the actual-position data are conveyed during the machining process in real time or the control data are conveyed before the beginning of the machining process or during the machining process in real time from a control unit of the machining head to an evaluation unit in order to provide information on the predefined welding or cutting path along which the laser beam is moved over the workpieces to be machined so that the course of the predefined welding or cutting path is used as prior knowledge for assessing the detector data, and wherein the laser-machining process is interrupted neither for the detection of radiation emitted by the workpieces nor for evaluating the detected radiation in the respectively selected detection field section (60, 68, 68', 78); c) evaluating the radiation (70, 70', 82, 82'), detected in a two-dimensionally spatially resolved manner, in the selected detection field section (60, 68, 68', 78); and d) detecting defects at the cutting edge or the weld seam on the basis of the radiation (70, 70', 82, 82') evaluated in the selected detection field section (60, 68, 68', 78). a) detecting, in a two-dimensionally spatially resolved manner, radiation (70, 70', 82, 82') emitted and/or reflected by the workpiece by means of a detector which is arranged in or on the machining head, characterized by the following steps: b) selecting at least one detection field section (60, 68, 68', 78) in changing positions in the detection field of the detector - on the basis of control data for controlling a movement of the laser beam along the predefined cutting or welding path or - on the basis of previously determined actual-position data of the laser beam along the welding or cutting path, wherein the actual-position data of the laser beam are determined on the basis of position coordinates of a deflector means arranged in the machining head about its pivot axes, wherein the actual-position data are conveyed during the machining process in real time or the control data are conveyed before the beginning of the machining process or during the machining process in real time from a control unit of the machining head to an evaluation unit in order to provide information on the predefined welding or cutting path along which the laser beam is moved over the workpieces to be machined so that the course of the predefined welding or cutting path is used as prior knowledge for assessing the detector data, and wherein the laser-machining process is interrupted neither for the detection of radiation emitted by the workpieces nor for evaluating the detected radiation in the respectively selected detection field section (60, 68, 68', 78); - on the basis of control data for controlling a movement of the laser beam along the predefined cutting or welding path or - on the basis of previously determined actual-position data of the laser beam along the welding or cutting path, wherein the actual-position data of the laser beam are determined on the basis of position coordinates of a deflector means arranged in the machining head about its pivot axes, wherein the actual-position data are conveyed during the machining process in real time or the control data are conveyed before the beginning of the machining process or during the machining process in real time from a control unit of the machining head to an evaluation unit in order to provide information on the predefined welding or cutting path along which the laser beam is moved over the workpieces to be machined so that the course of the predefined welding or cutting path is used as prior knowledge for assessing the detector data, and wherein the laser-machining process is interrupted neither for the detection of radiation emitted by the workpieces nor for evaluating the detected radiation in the respectively selected detection field section (60, 68, 68', 78); c) evaluating the radiation (70, 70', 82, 82'), detected in a two-dimensionally spatially resolved manner, in the selected detection field section (60, 68, 68', 78); and d) detecting defects at the cutting edge or the weld seam on the basis of the radiation (70, 70', 82, 82') evaluated in the selected detection field section (60, 68, 68', 78).