  We consider the possibility that the total dark energy (DE) of the Universe
is made out of two dynamical components of different nature: a variable
cosmological term, Lambda, and a dynamical ``cosmon'', X, possibly interacting
with Lambda but not with matter -- which remains conserved. We call this
scenario the LXCDM model. One possibility for X would be a scalar field, but it
is not the only one. The overall equation of state (EOS) of the LXCDM model can
effectively appear as quintessence or phantom energy depending on the mixture
of the two components. Both the dynamics of Lambda and of X could be linked to
high energy effects near the Planck scale. In the case of Lambda it may be
related to the running of this parameter under quantum effects, whereas X might
be identified with some fundamental field (say, a dilaton) left over as a
low-energy ``relic'' by e.g. string theory. We find that the dynamics of the
LXCDM model can trigger a future stopping of the Universe expansion and can
keep the ratio rho_D/rho_m (DE density to matter-radiation density) bounded and
of order 1. Therefore, the model could explain the so-called ``cosmological
coincidence problem''. This is in part related to the possibility that the
present value of the cosmological term can be Lambda<0 in this framework (the
current total DE density nevertheless being positive). However, a cosmic halt
could occur even if Lambda>0 because of the peculiar behavior of X as ``Phantom
Matter''. We describe various cosmological scenarios made possible by the
composite and dynamical nature of LXCDM, and discuss in detail their impact on
the cosmological coincidence problem.
