Asthenocotyle azorensis n. sp. (Monogenea: Microbothriidae) is described from the dermal denticles of the great lanternshark Etmopterus princeps Collett off the Azores. The type-species of the genus, A. kaikourensis Robinson, 1961, is redescribed and additional observations are made on A. taranakiensis Beverley-Burton, Klassen & Lester, 1987. The generic diagnosis is revised. The new species is distinguished from its two congeners by the large size of the pharynx and fewer testes. The ejaculatory bulb of A. kaikourensis is much larger than those of A. taranakiensis and A. azorensis and is supplied with many ducts from an extensive field of male accessory gland-cells located outside the genital pouch and extending posteriorly to the region of the germarium and external seminal vesicle. Asthenocotyle taranakiensis is distinguished from the other two species by its copulatory sclerite, which forms a double loop, although this may not be the case when the copulatory organ is extended. The bodies of A. azorensis and A. kaikourensis are similar in shape, with the maximum width approximately 37% and 25%, respectively, of the total length from the anterior end. In addition to the relatively small size of the genital pouch and ejaculatory bulb in A. azorensis and A. taranakiensis, the vaginal opening is adjacent to the common genital opening. In A. kaikourensis, the vaginal opening is distant from and posterior to the common genital opening. The functional morphology of the copulatory organ of A. azorensis is considered. The relative importance, for the taxonomy of microbothriids, of the number of testes versus the anatomy of the copulatory complex is discussed.