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A new theoretical framework for the evaluation of the in-band nonlinear distortion effects on the performance of OFDM systems is presented. In contrast to previous works that approximate the nonlinear noise as a Gaussian additive random process, the new framework is based on the properties of the large deviations of a stationary Gaussian process and shot noise theories, which can evaluate the performance of the OFDM system with high accuracy, especially at realistic scenarios where the Gaussian approximation of the nonlinear noise is no longer valid. The approach can be used to evaluate many communication systems with peak-limited nonlinearities and high PAPR, such as the downlink performance analysis of large capacity DS-CDMA systems.