This paper investigates parameter and order identification of a class of block-oriented nonlinear systems. By using the hierarchical identification principle, the system is divided into two subsystems, which are a linear block system and a nonlinear block system. For the purpose of solving the difficulty of estimating two sets of parameter vectors, the over-parameterization method and the key item separation technique are used, respectively. Therefore, a two-stage over-parameterization gradient-based iterative algorithm and a key term separation two-stage gradient-based iterative algorithm are derived. The simulation results indicate that the proposed algorithms are effective. Finally, the proposed method is evaluated through a battery model. The results show well agreement with the real system outputs.