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An efficient algorithm for detecting approximate tandem repeats in genomic sequences is presented. The algorithm is based on innovative statistical criteria to detect candidate regions which may include tandem repeats; these regions are subsequently verified by alignments based on dynamic programming. No prior information about the period size or pattern is needed. Also, the algorithm is virtually capable of detecting repeats with any period. An implementation of the algorithm is compared with the two state-of-the-art tandem repeats detection tools to demonstrate its effectiveness both on natural and synthetic data. The algorithm is available at www.cs.brown.edu/people/domanic/tandem/.