Summary: In this paper we study a nonlinear elliptic-parabolic system, which is motivated by mathematical models for lithium ion batteries. For the reliable and fast numerical solution of the system a reduced-order approach based on Proper Orthogonal Decomposition (POD) is applied. The strategy is justified by a priori error analysis for the error between the solution to the coupled system and its POD approximation. The nonlinear coupling is realized by variants of the empirical interpolation introduced by M. Barrault et al. [C. R., Math., Acad. Sci. Paris 339, No. 9, 667–672 (2004; Zbl 1061.65118)] and S. Chaturantabut and D. C. Sorensen [Application of POD and DEIM on a dimension reduction of nonlinear miscible viscous fingering in porous media. Techn. Rep. TR09-25, RICE Univ. (2009)]. Numerical examples illustrate the efficiency of the proposed reduced-order modeling.