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In an asynchronous direct-sequence code-division multiple-access, a specific bit of the reference user is interfered by two asynchronously arriving surrounding bits of all the other users supported by the system. Hence, for optimum multiuser detection, the entire input bit sequence influencing the current bit decisions must be considered, which results in a high detection delay as well as a high receiver complexity. Suboptimal multiuser-detection methods have been proposed based on a truncated observation window, in which the so-called "edge" bits are tentatively estimated by some other means. Using a similar approach, a multiuser detector is developed in this contribution that invokes genetic algorithms (GAs) in order to estimate both the desired bits as well as the edge bits within the truncated observation window. Using computer simulations, we showed that by employing GAs for improving the estimation reliability of the edge bits, our proposed multiuser detector is capable of achieving a near-optimum bit-error-rate performance, while imposing a lower complexity than the optimum multiuser detector.