Dynamic light scattering in the polarized geometry has been used to investigate the dynamics of composition fluctuations in solutions of two poly(styrene-block-1,4-isoprene) diblock copolymers in a nonselective, good solvent both far from and near to the ordering transition. Four different relaxation mechanisms were identified. One relaxation relates to the cooperative diffusion of copolymer chains, and it behaves similarly to that in semidilute homopolymer solutions. As concentration increases, two additional relaxations gain in amplitude : the wavevector-independent internal or breathing mode, predicted by theory, with amplitude increasing with scattering angle, and the recently established for copolymer melts diffusive relaxation; the relaxation times of both processes increase with copolymer concentration. In addition, another very slow process is evident at low scattering angles and is related to the long-range density fluctuations. A theoretical analysis is presented that predicts the existence and the behavior of the first three relaxations. The new diffusive relaxation is attributed to the composition polydispersity of the diblocks; its intensity is proportional to the degree of polydispersity; its rate is governed by the self-diffusion of the copolymer chains; both its intensity and its relaxation time increase with the copolymer concentration, in contrast to the behavior of the cooperative diffusion.