Adaptive filtering has been used in recent years in many areas such as control systems, prediction, system identification and modeling, signal processing, speech processing and communication systems. In order to implement the adaptive infinite impulse response (IIR) system identification problem efficiently, it is essential to calculate the optimal system parameters and select the identity structure. In this study, Firefly and Particle Swarm Optimization are used to calculate IIR optimal system parameters. In these algorithms, Integral Absolute Error (IAE) is chosen as the error criterion. The performance analysis was carried out by implementing the proposed methods in three different IIR systems. (Abstract)