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In this paper a population based evolutionary optimization methodology called firefly algorithm (FFA) is applied for the optimization of system coefficients of the infinite impulse response (IIR) system identification problem. FFA is inspired by the flash pattern and characteristics of fireflies. In FFA technique, behaviour of flashing firefly towards its competent mate is structured. In this algorithm attractiveness depends on brightness of light and a bright firefly feels more attraction for the brighter one. For this optimization problem, brightness varies inversely proportional to the error fitness value, so the position of the brightest firefly gives the optimum result corresponding to the least error fitness in multidimensional search space. Incorporation of different control parameters in basic movement equation results in balancing of exploration and exploitation of search space. The proposed FFA based system identification approach has alleviated from inherent drawbacks of premature convergence and stagnation, unlike genetic algorithm (GA), particle swarm optimization (PSO) and differential evolution (DE). The simulation results obtained for some well known benchmark examples justify the efficacy of the proposed system identification approach using FFA over GA, PSO and DE in terms of convergence speed, identifying plant coefficients and mean square error (MSE) fitness values produced for both same order and reduced order models of adaptive IIR filters.