The growth rate for instabilities in an expanding parton plasma is investig
ated by using a quasiparticle transport model including hadronization. The
coupled Boltzmann equations for partons and pions with time dependent mean
field masses and source terms are solved in the Bjorken boost invariant pic
ture. Hadronization modifies the known instability in the parton plasma cre
ated by the mean field in two ways: In the beginning, hadronization increas
es the rate Gamma of instability, but then Gamma --> 0 when the hadronizati
on is dominating the time evolution.