We introduce a new damage spreading algorithm which is able to capture both the long-time and short-time dynamics of extended systems which evolves towards a critical statistically stationary state. In this sense, the dynamics of systems exhibiting self-organized critical states is shown to be similar to the one observed at the usual critical point of continuous phase transitions and at the onset of chaos of nonlinear low-dimensional dynamical maps. The proposed algorithm is applied to the Bak-Sneppen model of biological evolution and the ballistic deposition model of surface growth. The critical dynamics of these models are discussed within the framework of a nonextensive statistics formalism. (C) 2004 Elsevier B.V. All rights reserved.