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The effect of nonlinear gain on the intensity noise of semiconductor lasers is studied by solving the single-mode rate equation with the Langevin noise term. The analytic expressions for the relative intensity noise and the intensity autocorrelation function are obtained by using a form of the nonlinear gain that is valid even at high operating power levels. These are used to obtain a simple expression for the signal-to-noise ratio (SNR) of the laser output. The SNR is found to saturate to a limiting value of about 30 dB at high powers because of the nonlinear-gain effects related to intraband gain saturation.