Topographic homology conjectures (= THCs) in fore- and hind wing venation of extant king crickets, raspy crickets and weta are re-evaluated. Based on the premises that topological homology is established so that the amount of transformation that has to be assumed to explain differences between patterns is minimized, a new set of THCs (= STHC), based on morphological data on the species cf. mexicanus de Saussure, 1859: 209, laudatum Johns, 1997, ornata Willemse, 1963, cf. bicornis Karny, 1929a, pinguipes? Rentz in Morton & Rentz, 1983, pinguipes Rentz in Morton & Rentz, 1983, an undetermined species, punctipennis Walker, 1869, and rufovaria Kirby, 1888, is elaborated. Among other transformations, the occurrence of a re-routing of MP along CuA (i.e., the basal M CuA stem splits into MA and MP CuA, instead of into MA MP and CuA) is demonstrated for pinguipes, punctipennis, and rufovaria. Concurrently, intra-specific variability in forewing venation is appreciated for laudatum, ornata, cf. bicornis, pinguipes, punctipennis, and rufovaria. A cladotypic-compliant nomenclatural scheme is elaborated based on the proposed THCs. The taxon Agryllacris nom.-dis.typ. nov. is defined based on the character state ‘in forewing, CuA CuPaα with two distal branches only’; the taxon Tagryllacris nom.-dis.-typ. nov. is defined based on the character state ‘in forewing, M CuA splits into MA and MP CuA’; the taxon Etagryllacris nom.-dis.-typ. nov. is defined based on the character state ‘in forewing, CuA CuPaα keep fused’; the taxon Metagryllacris nom. nov, dis. Zeuner, 1939, typ. nov. is defined based on the character state ‘in forewing, MA fused with R at wing base’. Based on new data, the species †perfecta Sharov, 1968 is identified as a member of the taxon Agryllacris, and the fossil species †megaptera Gorochov, 1987a, isimplicis Gorochov, 1987a, †elongata Gorochov, 1987a, †madygenioides Gorochov, 1987a, †perlonga Gorochov, 1987a, and † devexa Gorochov, 1987a are considered as junior synonyms of †perfecta. The nomenclatural treatment is extended to the unrelated taxon †Bintoniellidae nom. Handlirsch, 1938, dis. Sharov, 1968, typ. nov, defined based on the character state ‘in forewing, no distinct base of CuPaα diverging from CuPa (and fusing with CuA or M CuA)’. Belonging to this taxon, the species †primaria Sharov, 1968 is considered as a junior synonym † triassica Sharov, 1968:168.A consequence of the assignment of †perfecta to Agryllacris is that this group stems in the Triassic, at least, i.e., ca 170 million years earlier than previously assumed. As a result, the loss of the complex ‘tettigonid-gryllid-like’ (i.e., Grylloptera) stridulatory apparatus is no longer needed to account for the morphology of king crickets, raspy crickets and weta forewing. Finally, a refinement of the conce