In this report I discuss the theory of dynamical instabilities which may occur in relativistic heavy-ion collisions (RHIC), and their possible consequences. I confine myself to consideration of isoscalar instabilities in hadron matter, though it is predicted that such instabilities may take place in the spin-isospin mode~1 and in the quark-gluon plasma (QGP)~2. These instabilities in inequilibrium systems originate due to a specific dynamics of mean fields which simulteneously determine the nuclear equation of state in equilibrium. Therefore, by observing these instabilities one can learn a lot about the nuclear equation of state even in case the equilibrium is not actually reachedi n RHIC.
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