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In this paper, we study the problem of motif discoveries in unaligned DNA and protein sequences. The problem of motif identification in DNA and protein sequences has been studied for many years in the literature. Major hurdles at this point include computational complexity and reliability of the search algorithms. We propose a self-organizing neural network structure for solving the problem of motif identification in DNA and protein sequences. Our network contains several layers, with each layer performing classifications at different levels. The top layer divides the input space into a small number of regions and the bottom layer classifies all input patterns into motifs and nonmotif patterns. Depending on the number of input patterns to be classified, several layers between the top layer and the bottom layer are needed to perform intermediate classifications. We maintain a low computational complexity through the use of the layered structure so that each pattern's classification is performed with respect to a small subspace of the whole input space. Our self-organizing neural network will grow as needed (e.g., when more motif patterns are classified). It will give the same amount of attention to each input pattern and will not omit any potential motif patterns. Finally, simulation results show that our algorithm outperforms existing algorithms in certain aspects. In particular, simulation results show that our algorithm can identify motifs with more mutations than existing algorithms. Our algorithm works well for long DNA sequences as well.