  The propagation of short life time particles with consequently broad mass
width are discussed in the context of transport descriptions. In the first part
some known properties of finite life time particles such as resonances are
reviewed and discussed at the example of the $\rho$-meson. Grave deficiencies
in some of the transport treatment of broad resonances are disclosed and
quantified. The second part addresses the derivation of transport equations
which permit to account for the damping width of the particles. Baym's
$\Phi$-derivable method is used to derive a self-consistent and conserving
scheme, which fulfils detailed balance relations even in the case of particles
with broad mass distributions. For this scheme a conserved energy-momentum
tensor can be constructed. Furthermore, a kinetic entropy can be derived which
besides the standard quasi-particle part also includes contributions from
fluctuations.
