In this study, a hybrid method based on the marine predators algorithm (MPA) and adaptive neuro-fuzzy inference system (ANFIS) is presented to identify nonlinear systems exhibiting symmetrical or asymmetrical behavior. In other words, the antecedent and conclusion parameters of the ANFIS are adjusted by the MPA. The performance of the MPA is evaluated on eight nonlinear systems. The mean squared error is used as the error metric. Successful results were obtained on the eight systems. The best mean training error values belonging to the eight systems are 1.6 × 10⁻⁶, 3.2 × 10⁻³, 1.5 × 10⁻⁵, 9.2 × 10⁻⁶, 3.2 × 10⁻⁵, 2.3 × 10⁻³, 1.7 × 10⁻⁵, and 8.7 × 10⁻⁶. In the ANFIS training carried out to solve the related problems, the performance of the MPA was compared with the butterfly optimization algorithm, the flower pollination algorithm, moth–flame optimization, the multi-verse optimizer, the crystal structure algorithm, the dandelion optimizer, the RIME algorithm, and the salp swarm algorithm. The results have shown that the performance of the MPA mostly outperforms other algorithms in both training and testing processes.