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Steroid hormones are necessary for vital functions of most of vertebrates. Hormone molecules act within cells via interaction with their receptor proteins which are transcription factors. Identification of hormone response elements (HREs) in DNA is essential for understanding the mechanism of hormone-mediated gene expression regulation. We present a systematic approach for recognition of HREs within promoters of vertebrate genes. The proposed approach is based on an experimentally validated dataset and a specifically reconstructed cascade Markov model for HRE recognition with reference to its complex composition. The approach provides a reliable accuracy for HRE prediction, and may be extended to other sequence motifs with repeated or multi-component structure. The developed FPGA implementation of the Markov model is tested using a Virtex-4 board. The model is trained for prediction of HREs in promoters of hormone-responsive genes, and for further study on direct targets for androgen, progesterone and glucocorticoid hormones.