In multiagent dynamical systems, privacy protection corresponds to avoid disclosing the initial states of the agents while accomplishing a distributed task. The system-theoretic framework described in this paper for this scope, denoted dynamical privacy, relies on introducing output maps which act as masks, rendering the internal states of an agent indiscernible by the other agents. Our output masks are local (i.e., decided independently by each agent), time-varying functions asymptotically converging to the true states. The resulting masked system is also time-varying, and has the original unmasked system as its limit system. It is shown that dynamical privacy is not compatible with the existence of equilibria. Nevertheless the masked system retains the same convergence properties of the original system: the equilibria of the original systems become attractors for the masked system but lose the stability property. Application of dynamical privacy to popular examples of multiagent dynamics, such as models of social opinions, average consensus and synchronization, is investigated in detail. (c) 2020 Elsevier Ltd. All rights reserved.