Abstract.Some groups of insects, such as certain Ichneumonidae and fungus‐feeding Phlaeothripidae, appear to have undergone frequent reversal or parallelism (homoplasy) of characters during evolution so that extant species present almost every imaginable permutation and combination of characters. Recognition of holophyletic genera in such groups is difficult. Large monothetically defined genera are often not holophyletic, whilst small genera need to be defined by a large and invariable character‐suite. Any classification produced by adopting small genera will not possess one of the valuable attributes of the classical Linnaean system, its predictive ability; a large proportion of new species will require new genera. For groups exhibiting a high degree of homoplasy it is suggested that a polythetic classification be erected. Polythetic genera can be holophyletic groups and are not merely phenetic assemblages. The probability of correctly assigning a species (either a new one or when making an identification) is shown to be higher for a polythetic classification. A simple key device, the polyclave, is given to enable practical separation of two polythetic taxa. It is suggested that homoplasy, and its associated problems in classification, may be associated with a particular type of biology in which population size is not limited by direct competit