  We consider in this paper the well-posedness for the Cauchy problem
associated to two-dimensional dispersive systems of Boussinesq type which model
weakly nonlinear long wave surface waves. We emphasize the case of the {\it
strongly dispersive} ones with focus on the "KdV-KdV" system which possesses
the strongest dispersive properties and which is a vector two-dimensional
extension of the classical KdV equation.
