  We investigate a cosmological model in which dark energy, represented by a
quintessential scalar field, is directly coupled to a dark-matter perfect
fluid. We are interested in solutions of cosmological relevance, namely those
for which a dark-matter-dominated era long enough to allow for structure
formation is followed by an era of accelerated expansion driven by dark energy.
For the coupling between these two dark components of the Universe, we choose
forms that generalize the one most commonly used in the literature. Resorting
to powerful methods of qualitative analysis of dynamical systems, we show that,
for certain generalized forms of the coupling, final states of our coupled
quintessential model correspond to solutions in which the evolution of the
Universe is completely dominated by dark energy. In this case, there are no
scaling solutions. Interestingly, however, for certain values of a relevant
parameter, during the approach to the final state of evolution, the
cosmological parameters change so slowly that, for all practical purposes, the
solution appears to be stuck in a state corresponding to a scaling solution.
