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This paper presents a new technique for the design of IIR digital filters with simultaneous amplitude and group-delay requirements. The filter stability is guaranteed by controlling the poles' positions and the filter delay. This algorithm is based on genetic algorithm where the genetic parameters such as population size, number of generations, and crossover probability are adopted for designing filters with power of two, integer or real coefficients. The fitness function is defined as the simple reciprocal of sum squared of the magnitude and delay errors. The proposed method has been tested for the design of filters with different amplitude and group-delay specifications.