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Quasi-linearized multimode quantum-mechanical rate equations with shot-noise sources for nearly single-longitudinal-mode semiconductor lasers are solved analytically by means of a flow graph technique. It is found that mode partition noise is the major intensity noise at low frequencies. At the resonance frequency, the "single-mode" noise dominates. Expressions for the relative intensity noise at low frequencies and the resonance frequency are derived. The correlation of the main mode and a side mode is negative at low frequencies and positive at the resonance frequency. The analysis also shows that intensity fluctuations of a side mode have a time constant of a few nanoseconds and a weak resonance peak caused by the fluctuations of the carrier number.