Using a Lagrangian which contains quarks as elementary degrees of free
dom and mesons as bound states, a transport formalism is developed, wh
ich allows for a dynamical transition from a quark plasma to a state.
where quarks are bound into hadrons. Simultaneous transport equations
for both particle species are derived in a systematic and consistent f
ashion. For the mesons a formalism is used which introduces off-shell
corrections to the off-diagonal Green functions. It is shown that thes
e off-shell corrections lead to the appearance of elastic quark scatte
ring processes in the collision integral. The interference of the proc
esses <q(q)over bar>-->pi and <q(q)over bar>-->pi--><q(q)over bar> lea
ds to a modification of the s-channel amplitude of quark-antiquark sca
ttering.