We investigate the time evolution of a quark antiquark plasma by solving numerically the relativistic transport equations derived on the Hartree level from the Nambu-Jona-Lasinio model. We find that the phase transition in the expanding quark antiquark plasma is different as compared to that in a static plasma. The expansion competes with the transition and finally quark droplets will be formed which subsequently hadronizes. These findings raise the question whether static thermal models can make at all any prediction about signals of that transition .