Testing non-typified names by applying rules of circumscriptional nomenclature shows that in most cases the traditional usage can be supported. However, the original circumscription of several widely used non-typified names does not fit the taxa they are applied to. Here I discuss names historically applied to the taxa whose correct circumscriptional names should be Hexapoda, Amyocerata, Triplura, Dermatoptera, Saltatoria, Spectra, Pandictyoptera, Palaeoblattariae, Neoblattariae, Parametabola, Parasita, Arthroidignatha, Plantisuga, Metabola, Birostrata, Rhaphidioptera, Meganeuroptera, Eleuterata, Panzygothoraca, Lepidoptera and Glossolepidoptera. The new names Holopandictyoptera taxon nov., Cryptovipositoria taxon nov., Oothecophora taxon nov., Enteracantha taxon nov., and Pleuroptera taxon nov. are proposed for recognized but yet unnamed taxa.