Abstract: A method of machining workpieces with a laser beam wherein the machining cess, in particular the melting depth or the through-melting distance is monitored by detecting an optical and/or acoustical signal created by an unshielded laser-induced plasma or vapor. In order to receive monitoring date which as much as possible is independent of signal variations in the process the signals are subjected to a frequency analysis and the average amplitudes (Ax, Ay) of two different frequency bands (x, y) of the analyzed frequencies are used with a predetermined calculation function to determine a rating value (B).