We study the dynamical behavior of disordered many-particle systems with long-range Coulomb interactions by means of damage-spreading simulations. In this type of Monte-Carlo simulations one investigates the time evolution of the damage, i.e. the difference of the o ccupation numbers of two systems, subjected to the same thermal noise. We analyze the dependence of the damage on temperature and disorder strength. For zero disorder the spreading transition coincides with the equilibrium phase transition, whereas for finite disorder, we find an evidence for a dynamical phase transition well below the transition temperature of the pure system.