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This paper presents a flexible and efficient subband adaptive second-order Volterra filter (SBVF) structure for nonlinear system identification. The structure is first described in detail, where the underlying filter-bank scheme and adaptive filtering algorithms are explained, followed by a computational complexity analysis. Simulation results are then presented, showing that the proposed structure can achieve equal system-identification performance compared with that of a fullband second-order Volterra structure at a much-reduced complexity. In addition, the structure provides a more precise system model compared with that of a linear-only structure at a potentially similar computational expense. The results also demonstrate the suggested structure's ability to exploit a priori knowledge of the nature of the system nonlinearity through selectable nonlinear subband filtering, resulting in further complexity savings. The simulation results are experimentally verified under a practical acoustic-echo-cancellation scenario. It is shown that the SBVF structure can achieve up to a 10-dB lower mean-square error than that of a linear-only model at a comparable complexity.