This paper does not give a detailed description of the backbone of any one of the eight isospondylid species examined. Instead, selected data have been used in a discussion of the broad principles of vertebral variation, as seen in fishes of the order Isospondyli. This was considered to be of greater value than a catalogue of vertebral details for each of a small number of already wellknown species. Even so, sufficient has been said to enable any worker to identify the backbone of any one of the eight species, as well as to obtain a most discriminative description of the backbone of any other species of Isospondyli he may examine. A distinction is drawn between the countable vertebral characters, which are statistics for the precise measurement of vertebral variation, and the 'marker' characters, which provide the means for recognition 'on sight'. It is believed that vertebral characters of both kinds might be profitably employed in the study of different biological populations of the same species. The correlation between vertebral characters and other bodily features, such as keeled scales, position of fins and anus, and contour of body cavity, receives attention, and is related to metamerism. Finally, the occurrence of autogenus vertebral arches and the bifid condition of the neural spines in the isospondylid backbone is shown to be primitive and not restricted to the order.