A monitoring device (10) for a laser machining device (12) that has one or more laser beams (13) that are displaced along a predetermined adjustable trajectory (14, 16) along a workpiece (18) includes one or more sensors (20, 22) which monitor(s) the processing signal (24) of the machining process in a three-dimensional section (26). The one or more sensors (20, 22) activate an alarm device or interrupter (28) for the one or more laser beams (13) of the laser machining device (12) if the one or more process signals (24) in the section (26) exceed a predetermined threshold value or fall short of it, the one or more sensors (20, 22) being independent of the laser machining device (12).