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Direct applications of high-power diode lasers (HPDLs) like hardening, heat conduction welding of metals, and joining of polymers have already been demonstrated also in the industrial environment. Relatively low intensities in the range of 10/sup 3/ W cm/sup -2/ are sufficient for these applications. While the commercial HPDL systems are built on the basis of diode laser bars with 40 W output power, in the meantime a record continuous-wave-output power of 267 W per bar has been demonstrated. The achievable higher output power per bar will lead to enhanced applicability of HPDLs and thus to a further steep increase of their industrial use. Improved packaging technology, multiplexing the emission of single bars and coherent coupling as well as promising new diode laser structures like Z-shaped broad area emitters, is discussed. In this paper, emphasis is laid on the potential applicability of commercial HPDLs for metal working with elevated intensities up to 10/sup 5/ W cm/sup -2/, like oxygen cutting and the worldwide first deep-penetration HPDL-weld up to a sheet thickness of 6 mm in stainless steel. These results have been predicted by proper theoretical modeling. Strong reduction of phase space dimension takes place in convective-diffusive-type free boundary problems typical for thermal processing. This property makes it possible to construct approximate finite-dimensional dynamical systems being solvable with controlled error. Numerical solutions of the full problem are used to investigate the quality of the approximate model. Observable quantities of the technical processes like signals from monitoring devices are part of the solution and solutions to the inverse problem are given.