An efficient algorithm is presented for detecting approximate tandem repeats in genomic sequences. The algorithm is based on a flexible statistical model which allows a wide range of definitions of approximate tandem repeats. The ideas and methods underlying the algorithm are described and its effectiveness on genomic data is demonstrated. Categories and Subject Descriptors J.3 [Computer Applications]: Life and medical sciences; G.3.8 [Mathematics of Computing]: Probability and statistics--Probabilistic algorithms General Terms Algorithms, Experimentation Keywords tandem repeats, trf, teiresias, atr, pattern discovery, DNA repeats, DNA satellites