A method is described for the generation of coherent laser radiation in the extreme ultraviolet. Light is first produced in lasers that operate at relatively long wavelengths (400–700 nm) or the near ultraviolet (200–400 nm), and is then shifted to shorter wavelengths by the nonlinear optical process known as harmonic generation (or more generally optical frequency conversion). This procedure eliminates the often difficult search for a medium that has the necessary gain at the desired wavelengths by making use of lasers already available. (AIP)