The primary objective of this paper was to determine the extent and nature of interspecies differences in axon calibre and myelin sheath thickness and in the various relationships between these. Morphometric analysis of the axon perimeter-myelin sheath thickness relationship was performed on an equivalent nerve fibre population in a mammal, the rat, a bird, the chicken, an amphibian, the frog, a bony fish, the trout, and a cartilaginous fish, the dogfish. The abducent nerve was studied. It is especially suitable for this purpose because its fibres are closely similar in type and in peripheral distribution across the species studied. The relationship differed substantially between species. Differences were present in its setting, as described by the positions of the scatterplots, in the g ratio and in the regression and correlation data relating the parameters. Both parameters were markedly larger in the fish species than in all of the others. In addition, in rat, chicken, frog and trout, where large and small fibre classes could be differentiated clearly, the setting of the relationship between the two parameters was different for the two classes. In the main, variation in each of the parameters was greater between than within species. The larger fibres in the fish species were closely similar in axon perimeter and sheath thickness despite their long evolutionary separation. From this study and from others in the series, it may be concluded that there is no fixed or constant relationship between axon calibre and the thickness of the surrounding myelin sheath. Each nerve tends to have its own particular relationship and this differs between species.