  We explore quintessence models of dark energy which exhibit non-minimal
coupling between the dark matter and the dark energy components of the cosmic
fluid. The kind of coupling chosen is inspired in scalar-tensor theories of
gravity. We impose a suitable dynamics of the expansion allowing to derive
exact Friedmann-Robertson-Walker solutions once the coupling function is given
as input. Coupling functions that lead to self-interaction potentials of the
single and double exponential types are the target of the present
investigation. The stability and existence of the solutions is discussed in
some detail. The models are tested against the observational evidence.
