In conventional hierarchical clustering methods, any object can belong to only one class or cluster. We present here an application of the pyramidal classification method to biological objects, which illustrates the intuitively appealing idea that some objects may belong simultaneously to two classes. In a first step, we performed an all-by-all comparison of all the open reading frames in the genomes from S. cerevisiae, M. jannaschii, E. coli, H. influenzae and Synechocystis. In a second step, a series of connex classes was built, each connex class containing all those sequences that were linked by a Z-value (obtained after 100 sequence shufflings) greater than a given threshold. Finally, each connex class was submitted to a pyramidal classification. Three examples of such classifications are given, concerning two sets of multi-domains protein sequences and a family of aminoacyl-tRNA synthetases. They make it clear that the linear order among the classified objects that results from the pyramidal classification is useful in deciphering the multiple relationships that can exist between the objects under study. A program for calculating and displaying a pyramidal classification from a dissimilarity matrix is available from http:/(/)genome.genetique.uvsq.fr/Pyramids. The pyramidal classifications of the connex classes from the five organisms (intra- and inter-genomic comparisons) are available from http:/(/)www.gene-it.com under the family item.