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Results of experimental studies of the generation of coherent radiation in the XUV by high order optical nonlinearities in the rare gases are described. Fifth- and seventh-harmonic conversion and six wave mixing of harmonic pulses from an Nd:YAG laser were used to produce radiation at several discrete wavelengths between 38 and 76 nm. Experimental measurements of fifth-haxmonic conversion of pump pulses at 266.1 nm in helium are compared with theoretical predictions. Discrepancies between theory and experiment are observed at high laser powers, and the role of competing processes is discussed.