  This paper is devoted to the study of a nonlinear coupled system of two
Korteweg-de Vries equations in a periodic domain under the effect of an
internal damping term. The system was introduced Gear and Grimshaw to model the
interactions of two-dimensional, long, internal gravity waves propagation in a
stratified fluid. Designing a time-varying feedback law and using a Lyapunov
approach we establish the exponential stability of the solutions in Sobolev
spaces of any positive integral order.
