While the abundance of available sequenced genomes has led to many studies of regional heterogeneity in mutation rates, the co-variation among rates of different mutation types remains largely unexplored, hindering a deeper understanding of mutagenesis and genome dynamics. Here, utilizing primate and rodent genomic alignments, we apply two multivariate analysis techniques (principal components and canonical correlations) to investigate the structure of rate co-variation for four mutation types and simultaneously explore the associations with multiple genomic features at different genomic scales and phylogenetic distances.