Little attention has been paid to the suprageneric classification for conodonts and existing schemes have been formulated without attention to homology, diagnosis and definition. We propose that cladistics provides an appropriate methodology to test existing schemes of classification and in which to explore the evolutionary relationships of conodonts. The development of a multi-element taxonomy and a concept of homology based upon the position, not morphology, of elements within the apparatus provide the ideal foundation for the application of cladistics to conodonts. In an attempt to unravel the evolutionary relationships between ‘complex’ conodonts (prioniodontids and derivative lineages) we have compiled a data matrix based upon 95 characters and 61 representative taxa. The dataset was analysed using parsimony and the resulting hypotheses were assessed using a number of measures of support. These included bootstrap, Bremer Support and double-decay; we also compared levels of homoplasy to those expected given the size of the dataset and to those expected in a random dataset. The dataset was analysed in three hierarchical tranches, representing three levels of certainty concerning multi-element reconstructions and positional homologies. There is much agreement between the results derived from the three partitions, but some inconsistency, particularly in the precise composition of the three main evolutionary grades traditionally recognised (Prioniodontida, Prioniodinina, Ozarkodinina). This is considered to result from (a) the progressive inclusion of data that is increasingly uncertain and (b) the inclusion of increasingly distantly related taxa, introducing spurious hypotheses of homology. We tested for these by partitioning the dataset into the three main evolutionary grades and in each instance resolution was seen to increase substantially, especially among prioniodinins. Our concluding scheme of relationships is a tree derived from a compilation of the three component subtrees, which is directly compatible with the most-parsimonious trees derived from the initial second tranche analysis with the exception of the position of Hibbardella. This is compared in detail to the main extant schemes of suprageneric classification. A formal scheme of suprageneric classification is presented and the distribution of characters with respect to component clades is considered as a basis for identifying diagnostic characters.