The ichnogenus Tremichnus Brett was established for small round pits in echinoderm endoskeletons, principally crinoids. It is morphologically identical to Oichnus Bromley. It is significant that infestation of the echinoderm test is an integral part of any diagnosis of Tremichnus. This is an unacceptable ichnotaxobase; the diagnosis should only define morphology and, with reservation, substrate, such as unlithified (= soft), lithic or wood. From a recent revival of Tremichnus, Tremichnus paraboloides Brett is a junior homonym of Oichnus paraboloides Bromley; both share a similar morphology. Tremichnus puteolus Brett is more correctly referred to Lacrimichnus Santos et al. Tremichnus excavatus (Donovan and Jagt) could only be force-fitted into Tremichnus following a drastic revision of the original diagnosis and is here reassigned to Oichnus, as originally described.