The phylogenetic relationship among primates, ferungulates (artiodactyls + cetaceans + perissodactyls + carnivores), and rodents was examined using proteins encoded by the H strand of mtDNA, with marsupials and monotremes as the outgroup. Trees estimated from individual proteins were compared in detail with the tree estimated from all 12 proteins (either concatenated or summing up log-likelihood scores for each gene). Although the overall evidence strongly suggests ((primates, ferungulates), rodents), the ND1 data clearly support another tree, ((primates, rodents), ferungulates). To clarify whether this contradiction is due to (1) a stochastic (sampling) error; (2) minor model-based errors (e.g., ignoring site rate variability), or (3) convergent and parallel evolution (specifically between either primates and rodents or ferungulates and the outgroup), the ND1 genes from many additional species of primates, rodents, other eutherian orders, and the outgroup (marsupials + monotremes) were sequenced. The phylogenetic analyses were extensive and aimed to eliminate the following artifacts as possible causes of the aberrant result: base composition biases, unequal site substitution rates, or the cumulative effects of both. Neither more sophisticated evolutionary analyses nor the addition of species changed the previous conclusion. That is, the statistical support for grouping rodents and primates to the exclusion of all other taxa fluctuates upward or downward in quite a tight range centered near 95% confidence. These results and a site-by-site examination of the sequences clearly suggest that convergent or parallel evolution has occurred in ND1 between primates and rodents and/or between ferungulates and the outgroup. While the primate/rodent grouping is strange, ND1 also throws some interesting light on the relationships of some eutherian orders, marsupials, and montremes. In these parts of the tree, ND1 shows no apparent tendency for unexplained convergences.