  The effects of the propagation of particles which have a finite life-time and
an according broad distribution in their mass spectrum are discussed in the
context of a transport descriptions. In the first part some example cases of
mesonic modes in nuclear matter at finite densities and temperatures are
presented. These equilibrium calculations illustrate the dynamical range of
spectral distributions to be adequately covered by non-equilibrium description
of the dynamics of two nuclei colliding at high energies. The second part
addresses the problem of transport descriptions which properly account for the
damping width of the particles. A systematic and general gradient approximation
is presented in the form of diagrammatic rules which permit to derive a
self-consistent transport scheme from the Kadanoff--Baym equation. The scheme
is conserving and thermodynamically consistent provided the self-energies are
obtained within the Phi-derivable two-particle irreducible (2PI) method of
Baym. The merits, the limitations and partial cures of the limitations of this
transport scheme are discussed in detail.
