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A nonlinear stability analysis has been performed for mixed differential-integral equations particularly applicable to nuclear reactors. New general theorems of stability in bounded domains of initial perturbations have been introduced for a class of reactor models with an arbitrary reactivity feedback. Also, effective stability criteria have been established for reactors with linear reactivity feedbacks. For many kinds of models of phenomena typically encountered in nuclear reactors, these new criteria give sharper stability bounds than criteria previously published. The theoretical results obtained have been illustrated with examples of selected reactor models.