British and Irish species of the trilobite family Trinucleidae are investigated by numerical taxonomie methods. Forty-five attributes are defined, relating mainlyto the dorsal surface of the cephalon, and several of them representing new concepts. Of the 106 described species from the British Isles, 31 are fully codable on the basis of topo types. An analysis is based on these species, together with 28 partly topotypically codable species and samples of 9 other species (undescribed, non-topotypic or non-British). The relations of the species are depicted in an ordination derived by principal components analysis of the interattribute correlation matrix and with superimposed minimal spanning tree. On the basis of the ordination most of the analysed species can be grouped into two subfamilies, Trinucleinae and Cryptolithinae (including Marrolithinae); thersites is excluded from Reedolithinae. Trinucleinae and Cryptolithinae are strongly differentiated on the y1 axis of the ordination. The two subfamilies show parallel evolution during the Ordovician in general cranidial attributes (e.g. increasing length, declination of fringe). In Trinucleinae the fringe also shows evolutionary changes (e.g. increases in numbers and regularity of arcs); in Cryptolithinae the fringe evolves very little. Ordination of the attributes is by non-linear mapping based on a distance matrix derived from the interattribute correlation matrix by the transformation (tanh-1|r|)-1. Lectotypes of 12 species are here selected: albidus Reed, ceryx Lamont, gibbsii Salter, girvanensis Lamont, hibernicus Reed, inconstans Whittard, persulcatus Reed, praeterita Reed, rhodesi Whittard, sortita Reed, subradiatus Reed and thersites Salter.