A set of rate equations is derived describing the deterministic multi-mode dynamics of a semiconductor laser. Mutual interactions among the lasing modes, induced by high-frequency modulations of the carrier distribution, are described by carrier-inversion moments and lead to special spectral content of each spatial mode. The diffusion of carriers is shown to play an important role in determining the spectral properties of the field. The Bogatov effect of asymmetric gain suppression in semiconductor lasers will be derived. We will explicitly discuss the nontrivial relationship between the modes of the nonlinear cavity and the optical spectrum of the laser output and illustrate this for a two and three-mode laser.