The giant nerve fibres, which form so prominent a feature in the transverse section of the nerve cord of many Annelids, were first observed in these animals by Clapaède in 1861, who, however, regarded them as canals. They were first recognised as nervous elements—“riesige dunkelrandige Nervenfasern”—by Leydig in 1864. Since then their nervous nature has been almost alternately affirmed and denied, and many widely divergent views have been advanced regarding their morphology and function. The connection of giant fibres with certain giant nerve cells was first shown in the case of Halla parthenopeia , by Spengel, in 1881. Although many other workers have investigated these elements, information is still lacking regarding several fundamental points of their structure. For instance, nothing is known regarding the neurofibrillæ of the giant cells, and although these conducting elements have been seen by five observers in the giant fibres of earthworms, there is a striking difference in their accounts: two of them refer to the presence of several neurofibrillæ, while the others describe or figure only a single fibril in each giant fibre. Further, no information is available regarding the place and mode of origin of these neurofibrillæ or their relations to other nerve elements. This defect is, no doubt, due largely to the difficulties attending the investigation of these remarkable cells and fibres; indeed, the failure of the methods usually adopted for staining nerve cells and fibres in other animals, to disclose nervous elements in the giant cells and fibres, has been held, for instance, by yon Lenhossék and Retzius, to disprove their nervous nature. The present investigation was commenced in 1900 with the view of determining the character and arrangement of the neurofibrillæ of the giant cells and fibres and the relations of these elements to the other elements of the nerve cord.