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Blind equalizers avoid the transmission of pilot sequences, allowing a more efficient use of the channel bandwidth. Normally, after a first rough equalization is achieved, it is necessary to switch these equalizers to a decision-directed (DD) mode to reduce the steady-state mean-square error (MSE) to acceptable levels. The selection of an appropriate MSE threshold for switching between the blind and the DD modes is critical to obtain a good overall performance; however, this is not an easy task, since it depends on several factors such as the signal constellation, the communication channel, or the signal-to-noise ratio. In this paper, we propose an equalization scheme that adaptively combines a blind and a DD equalizers running in parallel. The combination is itself adapted in a blind manner, and as a result the overall scheme can automatically switch between the component filters, avoiding the need to set the transition MSE level a priori. The performance of our proposal is illustrated both analytically and through an extensive set of simulations, where we show its advantages with respect to existing hard- and soft-switching equalization schemes.