This work seeks to expose and clear up nomenclatural irregularities involving copepods of the order Monstrilloida, family Monstrillidae. The diagnostic text related to Monstrilla minuta Isaac, 1974 and four nominal species of Thaumaleus Krøyer, 1849 (now Cymbasoma Thompson, 1888) proposed by Isaac in 1974 is sufficient for all names to be available from their original description except for Thaumaleus similirostratus, which was proposed conditionally in 1974 and was first made available by Isaac in 1975; "similirostris" as used by Grygier in 1995 is an incorrect subsequent spelling. Four other specific names proposed in 1975 by Isaac, but disclaimed by him as nomina nuda (an action permitted retroactively by the Fourth Edition of the International Code of Zoological Nomenclature) have never been made available. By quoting the necessary information from Isaac's doctoral dissertation, two of them are validated herein under the names Thaumaleus frondipes Isaac in Grygier Suárez-Morales, sp. nov., and Strilloma scotti Isaac in Grygier Suárez-Morales, sp. nov., and are immediately reassigned as new combinations to Cymbasoma and Monstrilla Dana, 1849, respectively. A fifth such name, Thaumaleus tumorifrons, has already been made available under the authorship of Suárez-Morales, 1999, but its females are excluded from the type series; the spelling of the specific name of the new species recently proposed for those females, Cymbasoma mediterranea Suárez-Morales, Goruppi, Olazabal Tirelli, 2017, is emended to mediterraneum to match the gender of the genus. For Cymbasoma bowmani Suárez-Morales Gasca, 1998, the "Form B" female mentioned in the original description is excluded from the type series. The authorship and date of availability of Haemocera (currently Cymbasoma) morii depends on which language version of Article 13.1.1 of the Code is followed; a ruling by the International Commission on Zoological Nomenclature under Article 87 of the Code is necessary to resolve the matter. The composition of the type series of Cymbasoma bullatum (Scott, 1909) in terms of both number and sex has become unclear; its type locality is restricted herein to the vicinity of Obi Island in the Moluccas. Despite a published statement to the contrary, the syntype series of Cymbasoma germanicum (Timm, 1893) included specimens from other localities than just Helgoland. The type series of Cymbasoma guerrerense Suárez-Morales Morales-Ramírez, 2009 consists only of the holotype, which was mistakenly reported under the wrong registration number. The supposed invalidity of Monstrilla capitellicola Hartman, 1961 is discussed. Monstrilla javensis Isaac, 1974, nomen nudum, has remained unavailable owing to lack of adherence to Article 16.1 of the Code by later authors; the specific name is made available herein, under Suárez-Morales' authorship, in the combination Cymbasoma javense sp. nov. The taxonomic (and eventual nomenclatural) question of the status of M. mariaeugeniae Suárez-Morales Islas-Landeros, 1993 vis à vis M. wandelii Stephensen, 1913, i.e. as a separate species or a subspecies of the latter, remains unsettled. Cymbasoma lenticula Suárez-Morales McKinnon, 2014 and Monstrillopsis boonwurrungorum Suárez-Morales McKinnon, 2014 are fixed herein as the correct original spellings of those two specific names. Resolution of the problem posed by assignment of the specific name reticulata to supposedly non-conspecific males and females in the genus Monstrillopsis Sars, 1921 requires the designation of a neotype by the International Commission on Zoological Nomenclature.