In many eukaryotic genomes only a small fraction of the DNA codes for proteins, but the non-protein coding DNA harbors important genetic elements directing the development and the physiology of the organisms, like promoters, enhancers, insulators, and micro-RNA genes. The molecular evolution of these genetic elements is difficult to study because their functional significance is hard to deduce from sequence information alone. Here we propose an approach to the study of the rate of evolution of functional non-coding sequences at a macro-evolutionary scale. We identify functionally important non-coding sequences as Conserved Non-Coding Nucleotide (CNCN) sequences from the comparison of two outgroup species. The CNCN sequences so identified are then compared to their homologous sequences in a pair of ingroup species, and we monitor the degree of modification these sequences suffered in the two ingroup lineages. We propose a method to test for rate differences in the modification of CNCN sequences among the two ingroup lineages, as well as a method to estimate their rate of modification. We apply this method to the full sequences of the HoxA clusters from six gnathostome species: a shark, Heterodontus francisci; a basal ray finned fish, Polypterus senegalus; the amphibian, Xenopus tropicalis; as well as three mammalian species, human, rat and mouse. The results show that the evolutionary rate of CNCN sequences is not distinguishable among the three mammalian lineages, while the Xenopus lineage has a significantly increased rate of evolution. Furthermore the estimates of the rate parameters suggest that in the stem lineage of mammals the rate of CNCN sequence evolution was more than twice the rate observed within the placental amniotes clade, suggesting a high rate of evolution of cis-regulatory elements during the origin of amniotes and mammals. We conclude that the proposed methods can be used for testing hypotheses about the rate and pattern of evolution of putative cis-regulatory elements.