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A detailed theoretical analysis of nonresonant third harmonic generation (THG) is given which includes the intensity dependent refractive indices of the nonlinear medium as an integral part. According to the third-order analytic solution, the maximum attainable conversion efficiency is only limited by a nonlinear parameter β which is essentially the ratio of the Kerr-constants and the third harmonic coefficient. Only for intensity (energy) conversion efficiencies in excess of 90 percent (40 percent) are possible. The influence of the intensity distribution of the input beam is discussed. Diagrams are given from which the optimum experimental conditions can be deduced in order to get the optimum harmonic output. Limiting processes, such as fifth-order effects or self-focusing, are analyzed. As an example, the optimum conditions for efficient frequency tripling of powerful Nd:glass laser radiation are evaluated.