Based on a simple nonparametric procedure for comparing two proximity matrices, a measure of concordance is introduced that is appropriate when K independent proximity matrices are available. In addition to the development of a general concept of concordance and specific techniques for its evaluation within and between the subsets of a partition of the K matrices, several methods are also suggested for comparing and/or for fitting a particular structure to the given data. Finally, brief indications are provided as to how the well-known notion of concordance for K rank orders can be included within the more general framework.