A theoretical analysis of the correlation between mode fluctuations in a multilongitudinal mode laser is presented. The rate equations driven by Langevin noise sources are used to derive the correlation coefficients. By taking nonlinear terms into account, this analysis also applies to lasers with few modes and permits the derivation of the correlation coefficients from the the amplitude of these modes. They are found to be different from one pair of modes to another and to have not only negative, but also positive values. The fluctuations of a given mode are found to be concentrated in the low-frequency range, and the associated time constants are of great importance in the estimation of the partition noise for a signal propagating through a dispersive fiber.