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Calculations are presented which describe approximately the behavior of optically bistable devices based on the self-focusing of light. A simple heuristic calculation and a more complicated calculation which incorporates saturation of the material nonlinearity are presented. Both give a good qualitative description of situations in which a single hysteresis loop is observed. More complicated types of behavior, some of which have been observed, are predicted by the calculations which incorporate saturation. The results provide useful guides for the design of such devices.