Composite structures which show magneto-electric (ME) coupling behavior have a wide range of engineering applications. In this work, a composite structure comprising of a ferroelectric and a magnetostrictive material is taken for investigation. First, the nonlinear responses of the ferroelectric material and the magnetostrictive material are studied separately by experiments. In order to predict the nonlinear response, a thermodynamically consistent macroscopic model is proposed for the ferroic materials. Model parameters are then estimated from the experimental data, and the simulated results based on the proposed model are presented. Results from the theoretical model are in agreement with the experimental data. Subsequently, a homogenization procedure is introduced to find out the nonlinear response of a layered ME composite structure, and the obtained results are discussed. © 2017, Springer-Verlag Wien.