We consider the thermodynamical and hydrodynamical stabilities of proposed mechanisms for the dynamical hadronization transition in both ultrarelativistic heavy-ion collisions and the very early universe. We develop very general criteria for hydrodynamical stability and apply them to a number of proposed solutions. We find that the hadronization is accomplished by deflagration solutions in both scenarios. We argue that hadronization will occur before the quark-gluon plasma reaches a temperature that is low enough to admit detonations.