In order to clarify some controversial phylogenies such as those regarding the triplet of human, rodent, and cow and the evolutionary position of Lagomorpha with respect to other mammals, we have analyzed both nuclear and mitochondrial genes using the stationary Markov model developed in our laboratory. We found that the two sets of genes give different results. In particular the mitochondrial tree showed rabbit linked first to rodents and the rabbit-rodents branch linked to artiodactyls with human as the outgroup. The most favorite nuclear tree showed human linked first to artiodactyls and the human-artiodactyls branch linked to rabbit with rodents as the outgroup. The obvious questions, (1) which tree is the correct one, or (2) both trees can be incorrect, and (3) how can we explain such an evolutionary pattern, are discussed on the basis of our limited knowledge of factors that influence the clocklike behavior of biological macromolecules.