A machining apparatus for laser machining a workpiece, in particular for laser cutting, having a machining laser source configured to generate a machining laser beam; an illumination laser source having a power configured to generate an illumination laser beam having a spectral range; an outlet opening for the machining laser beam and the illumination laser beam; and a laser beam guiding device configured to guide the machining laser beam and the illumination laser beam coaxially through the outlet opening; wherein the laser beam guiding device comprises at least one transport fibre and at least one optical unit for focusing at least one element selected from the machining laser beam and the illumination laser beam; wherein the optical unit is dispersive; wherein the power of the illumination laser source and the spectral range of the illumination laser beam are chosen to generate an illumination by the illumination laser beam which is brighter than a self-emission of the workpiece in a machining region during laser machining; characterized in that the power of the illumination laser source is at least 50 mW, the central wavelength of the spectral range of the illumination laser beam is in the range 300 to 1000 nm, and the spectral range of the illumination laser beam is a wavelength band having a width of less than 20 nm; at least one element selected from the laser beam guiding device, the optical unit, the machining laser source and the illumination laser source is configured to generate a focus of the illumination laser beam and a focus of the machining laser beam which are axially apart from one another; the machining laser source and the illumination laser source are configured to generate different spectral ranges of the laser beams (14,16) generated thereby; the spectral range of the machining laser beam includes a first wavelength and the spectral range of the illumination laser beam includes a second wavelength less than the first wavelength; the at least one transport fibre is configured to guide the machining laser beam and the illumination laser beam coaxially; the transport fibre has an inner fibre core; the machining laser source and the illumination laser source are coupled to the transport fibre to guide the machining laser beam through the inner fibre core; the transport fibre has an outer fibre core enclosing the inner fibre core and/or a fibre cladding enclosing the inner or outer fibre core; and the machining laser source and the illumination laser source are coupled to the transport fibre to guide the illumination laser beam at least partially through at least one element selected from the outer fibre core and the fibre cladding. an illumination laser source having a power configured to generate an illumination laser beam having a spectral range; an outlet opening for the machining laser beam and the illumination laser beam; and a laser beam guiding device configured to guide the machining laser beam and the illumination laser beam coaxially through the outlet opening; wherein the laser beam guiding device comprises at least one transport fibre and at least one optical unit for focusing at least one element selected from the machining laser beam and the illumination laser beam; wherein the optical unit is dispersive; wherein the power of the illumination laser source and the spectral range of the illumination laser beam are chosen to generate an illumination by the illumination laser beam which is brighter than a self-emission of the workpiece in a machining region during laser machining; characterized in that the power of the illumination laser source is at least 50 mW, the central wavelength of the spectral range of the illumination laser beam is in the range 300 to 1000 nm, and the spectral range of the illumination laser beam is a wavelength band having a width of less than 20 nm; at least one element selected from the laser beam guiding device, the optical unit, the machining laser source and the illumination laser source is configured to generate a focus of the illumination laser beam and a focus of the machining laser beam which are axially apart from one another; the machining laser source and the illumination laser source are configured to generate different spectral ranges of the laser beams (14,16) generated thereby; the spectral range of the machining laser beam includes a first wavelength and the spectral range of the illumination laser beam includes a second wavelength less than the first wavelength; the at least one transport fibre is configured to guide the machining laser beam and the illumination laser beam coaxially; the transport fibre has an inner fibre core; the machining laser source and the illumination laser source are coupled to the transport fibre to guide the machining laser beam through the inner fibre core; the transport fibre has an outer fibre core enclosing the inner fibre core and/or a fibre cladding enclosing the inner or outer fibre core; and the machining laser source and the illumination laser source are coupled to the transport fibre to guide the illumination laser beam at least partially through at least one element selected from the outer fibre core and the fibre cladding.