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Coupled resonator filters (CRFs) are the new generation of BAW filters recently designed for the front-end modules of mobile transmission systems. Looking for designers' requirements, CRF devices have been characterized and modeled. The model based on equivalent circuits relies on material constants such as stiffness and electro-coupling coefficients, and works only for linear-mode propagation. Because of their positions between antennas and power amplifiers, they often work under high RF power, inducing nonlinear response in the AlN piezoelectric layer. In this work, we analyze for the first time the nonlinear behavior of AlN material particularly for coupled BAW resonators. To characterize the nonlinear effects in CRFs, we measure the 1-dB gain compression point (P1dB) and the intercept point (IP3). Then, we develop a nonlinear model of CRFs using harmonic balance (HB) simulation in commercially available software. The HB environment allows fitting simulations to measurements in terms of P1dB and IP3. We find that a high RF power induces nonlinear changes in the material constants' real parts: elastic stiffness c33 (4.9%), piezoelectric e33 (17.4%), and permittivity ε33 (5.2%). These nonlinear variations of material constants describe the nonlinear behavior of CRF devices using the same deposit process for AlN material.