Two parasitic copepods, Lateracanthus quadripedis Kabata & Gusev, 1966 and Parabrachiella annulata (Markevich, 1940) (Lernaeopodidae), were found on a deep-sea rudis rattail, Coryphaenoides rudis Günther, 1878 (Macrouridae) collected from the Xingang fishing port in Chenggong Town, Taitung County, in south-eastern Taiwan. Lateracanthus quadripedis was found attached to the walls of the branchial cavity of the fish, whereas P. annulata was collected from the body surface. This paper also provides a full description of these two copepod species to elucidate possible geographical variations in their morphology. Remarkably, our specimens of both copepods are more similar to those from the Galápagos Islands than to those from the Aleutian-Deep or Japan.