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In this paper, we propose a blind adaptive equalization scheme for time-varying channels, which combines a blind algorithm based on high order statistics (HOS) and decision-directed (DD) LMS algorithm. In contrast to the ldquostop-and-gordquo algorithm , where DD-LMS adaptation is stopped for unreliable decisions, the proposed algorithm applies a blind algorithm based on HOS for the unreliable decisions. Furthermore, the region of reliable decisions is updated corresponding to the estimated signal quality. Hence, the proposed ldquorun-and-gordquo algorithm inherits MMSE performance of DD-LMS and the (re)acquisition ability of the blind algorithm. Especially, for decision feedback equalizers (DFEs) the proposed algorithm provides robust blind initialization and reacquisition ability under time varying multipath environments.