In this paper the Genetic Algorithm (GA) is used to design and optimize a dual-band antenna system covering the UHF and VHF bands. The system contains two stacked vertical wire dipoles, one for each of the bands, above a perfectly-conducting ground plane. Unlike the case of the GA design of a single-band antenna [1, 2], the mutual coupling between the two dipoles introduces some complications in the design of dual-band antennas. Specifically, in the process of broad-banding one dipole by optimizing its loading and matching network for its own frequency band, it becomes necessary to take into account the influence of the second dipole operating in a different frequency band. It is, therefore, essential to carry out the analysis and the synthesis of the entire coupled system concurrently. This paper proposes a design procedure for the dual-band antenna system that makes initial choices for the antenna configuration on the basis of a systematic screening of the potential candidates, and then goes on to apply the GA in conjunction with the Numerical Electromagnetics Code (NEC4) [3] to meet the specifications for the two operating in a simultaneous manner.