In this paper, a comparative study of the dynamic scattering properties of some linear and cyclic copolymers in solution is presented. This investigation is prompted by the recent elastic and quasielastic light scattering measurements reported by Amis and co-workers on polystyrene-polydimethylsiloxane cyclic diblock copolymers and their linear triblock counterpart. A formalism is presented which could provide a theoretical framework for the analysis of some aspects of these data. The model predicts that two relaxation modes characterize the dynamics of both the cyclic diblock and the linear triblock copolymers. The amplitudes and decay rates of these relaxation modes are investigated as a function of the polymer architecture, the concentration, and the scattering wavevector. Questions related with phase transitions via aggregation or micellar formation are not addressed here.