AbstractThe peduncle lobe of Octopus, a centre concerned with regulating motor behaviour primarily on the basis of visual cues, though it also receives a “labyrinthine” or statocyst input, has been examined for the first time in the electron microsope. In the lower part of the lobe, the basal zone, there are large “motor” cells up to 20 μm across with a rounded, pale nucleus and a large perikaryon; there are also smaller cells, 4‐10 μm in diameter with a dark irregularly‐shaped nucleus. The latter receive synapses from afferent fibres to the lobe, and those from the principal afferent source, the ipsilateral optic lobe, have been characterised as large terminals with many small clear vesicles. Other optico‐peduncular afferents and the small‐cell fibres themselves run directly up to the second part of the lobe, the peduncle spine, which contains exclusively small granular cells about 5 μm in diameter. The fibres of these spine cells form a conspicuous and characteristic array of parallel fibres in the neuropil and they bear a striking resemblance to those of vertebrate cerebellar granule cells: serial synaptic relays are present along their length. These findings, together with earlier evidence about the effects on motor behaviour of lesions to the lobe, suggest a close functional and morphological analogy to a folium of the vertebrate cerebellum. The hypothesis is discussed that parallel fibres, with their narrow diameter and hence long conduction time, are an essential feature of fine motor control systems, and that their primary function is one of providing critical time delays in the millisecond range.