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Abstract. In this paper, an asymmetric version of the k-means clustering algorithm is proposed. The asymmetry arises caused by the use of asymmetric dissimilarities in the k-means algorithm. Application of asymmetric measures of dissimilarity is motivated with a basic nature of the k-means algorithm, which uses dissimilarities in an asymmetric manner. Clusters centroids are treated as the dominance points governing the asymmetric relationships in the entire cluster analysis. The results of experimental study on the real data have shown the superiority of asymmetric dissimilarities employed for the k-means method over their symmetric counterparts.