The paper is the first of a series, which aims to present a consistent interpretation of the suprageneric taxa of fossil beetles in the current century and their generic and species composition. Order Coleoptera is considered in composition of the superorder Coleopteroidea Handlirsch, 1903 (= Coleopterida sensu Boudreaux, 1979, nec Pearse, 1936) together with orders Skleroptera and Strepsiptera, and also with the family Umenocoleidae of unclear position. This paper includes the archostematan superfamilies Coleopseoidea and Cupedoidea of the infraorder Cupediformia, i.e., Coleopseidae (one genus and one species), Tshekardocoleidae (12 genera, 15 species), Labradorocoleidae (one genus, one species), Permocupedidae (together with Taldycupedinae, stat. nov., 24 genera and 54 species) and Cupedidae (three subfamilies, 49 genera, 253 species). The preliminary information on structure of the larva of Tshekardocoleidae from Tshekarda is done. There are also described the new taxa: genus Afrotaldycupes Kirejtshuk, gen. nov. with the type species: genus Taldycupes africanus Ponomarenko in Ponomarenko & Mostovski, 2005 [Afrotaldycupes africanus comb. nov.] and Afrotaldycupes lidgettoniensis (Ponomarenko in Ponomarenko & Mostovski, 2005), comb. nov. [Taldycupes]; genus Allophalerus Kirejtshuk, gen. nov. with the type species: Tetraphalerus aphaleratus Ponomarenko, 1969 [Allophalerus aphaleratus comb. nov.], and also with Allophalerus antiquus (Ponomarenko, 1964), comb. nov. [Tetraphalerus], Allophalerus bontsaganensis (Ponomarenko, 1997), comb. nov. [Tetraphalerus], Allophalerus incertus (Ponomarenko, 1969), comb. nov. [Tetraphalerus], Allophalerus latus (Tan, Ren et Shih, 2007), comb. nov. [Tetraphalerus], Allophalerus maximus (Ponomarenko, 1968), comb. nov. [Tetraphalerus], Allophalerus okhotensis (Ponomarenko, 1993), comb. nov. [Tetraphalerus], Allophalerus tenuipes (Ponomarenko, 1964), comb. nov. [Tetraphalerus], Allophalerus verrucosus (Ponomarenko, 1966), comb. nov. [Tetraphalerus]; genus Bukhkalius Kirejtshuk et Jarzembowski, gen. nov. with the type species: Tetraphalerus lindae Jarzembowski, Wang et Zheng, 2017 [Bukhkalius lindae comb. nov.]; genus Burmocoleus Kirejtshuk, gen. nov. with the type species: Burmocoleus prisnyi sp. nov. and Burmocoleus zhiyuani (Liu, Tan, slipinski, Jarzembowski, Wang, Ren et Pang, 2017), comb. nov. [Brochocoleus]; genus Cionocups Kirejtshuk, gen. nov. with the type species: Cionocups manukyani sp. nov.; genus Echinocups Kirejtshuk et Jarzembowski, gen. nov. with the type species: Notocupes neli Tihelka, Huang et Cai, 2020 [Echinocups neli comb. nov.], and also Echinocups ohmkuhnlei (Jarzembowski, Wang et Zheng, 2020), comb. nov. [Notocupes] and Echinocups denticollis (Jiang, Li, Song, Shi, Liu, Chen et Kong, 2020), comb. nov. [Notocupes]; genus Jarzembowskops Kirejtshuk, gen. nov. with the type species: Brochocoleus caseyi Jarzembowski, Wang et Zheng, 2016 [Jarzembowskops caseyi comb. nov.]; genus Lobanovia Kirejtshuk, gen. nov. with the type species: Simmondsia permiana Ponomarenko, 2013 [Lobanovia permiana comb. nov.]; genus Pintolla Kirejtshuk, gen. nov. with the type species: Kaltanicupes ponomarenkoi Pinto, 1987 [Pintolla ponomarenkoi comb. nov.]; genus Polyakius Kirejtshuk, gen. nov. with the type species: Polyakius alberti Kirejtshuk, sp. nov. and Polyakius pubescens Kirejtshuk, sp. nov.; Clessidromma zengi Kirejtshuk, sp. nov.; Cupes golovatchi Kirejtshuk, sp. nov.; Cupes legalovi Kirejtshuk, sp. nov.; Cupes lutzi Kirejtshuk, sp. nov.; Cupes nabozhenkoi Kirejtshuk, sp. nov. ; Cupes wedmannae Kirejtshuk, sp. nov. ; Mallecupes prokini Kirejtshuk, sp. nov. and Omma janetae Kirejtshuk, sp. nov. The new synonymy is established for the generic names Clessidromma Jarzembowski, Wang et Zheng, 2017 and Lepidomma Jarzembowski, Wang et Zheng, 2019, syn. nov. The rank of Cainomerga A. Kirejtshuk, Nel et P. Kirejtshuk, 2016 is elevated from subgeneric to generic. Also other new combinations are proposed: Cainomerga brevicornis (A. Kirejtshuk, Nel et P. Kirejtshuk, 2016), comb. nov. [Mesocupes], Cainomerga fraterna (A. Kirejtshuk, Nel et P. Kirejtshuk, 2016), comb. nov. [Mesocupes], Cainomerga immaculata (Piton, 1940: 194), comb. nov. [Zonabris, Mesocupes], Cainomerga palaeocenica (A. Kirejtshuk, Nel et P. Kirejtshuk, 2016), comb. nov. [Mesocupes], and Cainomerga ponti (A. Kirejtshuk, Nel et P. Kirejtshuk, 2016), comb. nov. [Mesocupes], Clessidromma tianae (Jarzembowski, Wang et Zheng, 2019), comb. nov. [Lepidomma], Diluticupes applanatus (Tan et Ren, 2009), comb. nov. [Brochocoleus], Diluticupes crowsonae (Jarzembowski, Yan, Wang et Zhang. 2013), comb. nov. [Brochocoleus], Diluticupes magnus (Tan et Ren, 2009), comb. nov. [Brochocoleus], Diluticupes minor (Ponomarenko, 2000), comb. nov. [Brochocoleus], Diluticupes validus (Tan et Ren, 2009), comb. nov. [Brochocoleus], Diluticupes yangshuwanziensis (Jarzembowski, Yan, Wang et Zhang. 2013), comb. nov. [Brochocoleus], Monticupes curtinervis (Tan, Ren et Shih, 2007), comb. nov. [Tetraphalerus], Monticupes decorosus (Tan, Wang, Ren et Yang, 2012), comb. nov. [Tetraphalerus], Odontomma sulcatum (Tan, Ren et Shih, 2007), comb. nov. [Brochocoleus], Omma ancistrodontum (Tan, Wang, Ren et Yang, 2012), comb. nov. [Pareuryomma], Omma grande (Ponomarenko, 1964), comb. nov. [Tetraphalerus], Omma longicolle (Ponomarenko, 1997), comb. nov. [Tetraphalerus], Pareuryomma angustum (Tan, Ren et Shich, 2007), comb. nov. [Brochocoleus], Pareuryomma magnum (Tan et Ren, 2009), comb. nov. [Brochocoleus], Zygadenia aliena (Tan et Ren, 2006), comb. nov. [Ovatocupes], Zygadenia baojiatunensis (Hong 1992), comb. nov. [Chengdecupes], Zygadenia brachycephala (Ponomarenko, 1994), comb. nov. [Notocupes], Zygadenia caduca (Ponomarenko, 1969), comb. nov. [Notocupes], Zygadenia caudata (Ponomarenko, 1966), comb. nov. [Notocupes], Zygadenia cellulosa (Ponomarenko, 1969), comb. nov. [Notocupes], Zygadenia crassa (Ponomarenko, 1969), comb. nov., [Notocupes], Zygadenia cyclodontus (Tan, Ren, Shih et Ge, 2006), comb. nov. [Amblomma, Notocupes], Zygadenia dischdes (Zhang, 1986), comb. nov. [Notocupes], Notocupes dundulaensis (Ponomarenko, 1994), comb. nov. [Notocupes], Zygadenia elegans (Ponomarenko, 1994), comb. nov. [Notocupes], Zygadenia epicharis (Tan, Ren et Liu, 2005), comb. nov. [Amblomma, Notocupes], Zygadenia eumeura (Tan, Ren et Liu, 2005), comb. nov. [Amblomma, Notocupes], Zygadenia excellens (Ponomarenko, 1966), comb. nov. [Notocupes], Zygadenia exigua (Ponomarenko, 1994), comb. nov. [Notocupes], Zygadenia foersteri (Ponomarenko, 1971), comb. nov. [Procarabus, Notocupes], Zygadenia homora (Lin, 1986), comb. nov. [Conexicoxa, Notocupes], Zygadenia issykkulensis (Ponomarenko, 1969), comb. nov. [Notocupes], Zygadenia jurassica (Hong 1983), comb. nov. [Chengdecupes], Zygadenia kezuoensis (Hong 1987), comb. nov. [Chengdecupes], Zygadenia khasurtuiensis (Strelnikova, 2019), comb. nov. [Notocupes], Zygadenia khetanensis (Ponomarenko, 1993), comb. nov. [Notocupes], Zygadenia kirghizica (Ponomarenko, 1969), comb. nov. [Notocupes], Zygadenia laeta (Lin, 1976), [Tetraphalerus], Zygadenia laiyangensis (Hong et Wang, 1990), comb. nov. [Forticupes, Notocupes], Zygadenia lapidaria (Ponomarenko, 1968), comb. nov. [Notocupes], Zygadenia laticella (Ponomarenko, 1969), comb. nov. [Notocupes], Zygadenia lata (Ponomarenko, 1969), comb. nov. [Notocupes], Zygadenia lenta (Ren, Lu, Guo et Ji, 1995), comb. nov. [Tetraphalerus], Zygadenia lini (Ponomarenko, Yan, Wang et Zhang, 2012), comb. nov. [Notocupes], Zygadenia longicollis (Ponomarenko, 1994), comb. nov. [Notocupes], Zygadenia ludongensis (Wang et Liu, 1996), comb. nov. [Notocupes], Zygadenia minuscula (Tan, Ren, Shih et Ge, 2006), comb. nov. [Amblomma, Notocupes], Zygadenia mongolica (Ponomarenko, 1994), comb. nov. [Notocupes], Zygadenia nigrimonticola (Ponomarenko, 1968), comb. nov. [Notocupes], Zygadenia oxypyga (Ponomarenko, 1969), comb. nov. [Notocupes], Zygadenia patula (Ponomarenko, 1985), comb. nov. [Notocupes], Zygadenia pingi (Ponomarenko et Ren, 2010), comb. nov. [Notocupes], Zygadenia porrecta (Tan, Ren, Shih et Ge, 2006), comb. nov. [Amblomma, Notocupes], Zygadenia protensa (Tan, Ren, Shih et Ge, 2006), comb. nov. [Amblomma, Notocupes], Zygodenia psilata (Tan, Ren et Liu, 2005), comb. nov. [Amblomma, Notocupes], , Zygadenia pulchra Ponomarenko, 1968, comb. nov. [Notocupes], Zygadenia reticulata (Oppenheim, 1888), comb. nov. [Procarabus, Notocupes], Notocupes rostrata (Ponomarenko, 1969), comb. nov. [Notocupes], Zygadenia rudis (Tan, Ren et Liu, 2005), comb. nov. [Amblomma, Notocupes], Zygadenia shiluoensis (Hong 1984), comb. nov. [Chengdecupes], Zygadenia sogutensis (Ponomarenko, 1969), comb. nov., Zygadenia stabilis (Tan, Ren et Liu, 2005), comb. nov. [Amblomma, Notocupes], Zygadenia tenuis (Ponomarenko, 1969), comb. nov. [Notocupes], Zygadenia tripartita (Oppenheim, 1888), comb. nov. [Procarabus, Notocupes], Zygadenia tuanwangensis (Hong et Wang, 1990), comb. nov. [Picticupes, Notocupes], Zygadenia valida (Lin, 1976), comb. nov. [Sinocupes, Notocupes], Zygadenia vitimensis (Ponomarenko, 1966), comb. nov. [Notocupes].
