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This paper introduces a novel blind equalization algorithm for frequency-selective channels based on a Bayesian formulation of the problem and the sequential importance sampling (SIS) technique. SIS methods rely on building a Monte Carlo (MC) representation of the probability distribution of interest that consists of a set of samples (usually called particles) and associated weights computed recursively in time. We elaborate on this principle to derive blind sequential algorithms that perform maximum a posteriori (MAP) symbol detection without explicit estimation of the channel parameters. In particular, we start with a basic algorithm that only requires the a priori knowledge of the model order of the channel, but we subsequently relax this assumption and investigate novel procedures to handle model order uncertainty as well. The bit error rate (BER) performance of the proposed Bayesian equalizers is evaluated and compared with that of other equalizers through computer simulations.