Informally, the zero-range'' particle system follows a collection of dependent random walks on a lattice, each of which interacts infinitesimally only with those particles already present at its location. In this talk, we consider the asymptotics of a distinguished, or tagged particle in this interacting particle system. In particular, we discuss anonequilibrium’’ invariance principle, in one dimension when the transition rates are mean-zero, with respect to a diffusion whose coefficients depend on the ``hydrodynamic’’ density.