We present a new algorithm capable of partitioning sets of objects by taking simultaneously into account their relational descriptions given by multiple dissimilarity matrices. The algorithm uses a nonlinear aggregation criterion, weighted Tchebycheff distances, more appropriate than linear combinations (such as weighted averages) for the construction of compromise solutions. We obtain a partition of the set of objects, the prototype of each cluster and a weight vector that indicates the relevance of each criterion in each cluster. Since this is a clustering algorithm for relational data, it is compatible with any distance function used to measure the dissimilarity between objects. Some practical applications are shown, the good results obtained indicate the interest of the presented algorithm.