Several specimens of the remarkable finned octopod Cirrothauma recently caught are described. The animal is taken at great depths, often near the bottom but sometimes away from it. The enormous arms and web can be spread to give a medusoid form but the animal also swims horizontally mainly using the fins, whose powerful muscles are attached to a large fin support. The animal is gelatinous and perhaps neutrally buoyant, and can almost certainly hover in the medusoid form. The mantle muscles are weak and the funnel very long. The arms are long and have a few small suckers in a single longitudinal row, only some of which have a minute suction chamber. The infundibula are small but the cuticle has small pegs with innumerable pores. The cuticle is closely similar to that of octopods and is capable of adhesion. In the base of each sucker peduncle, male and female, there is a possible light organ. The beaks are large and black, the lower strongly pointed. There is a large tongue with vestiges of a radula. The salivary papilla carries the duct of the `posterior salivary gland' which lies far forward within the buccal complex. The male ducts are simple and produce simple packets of sperms. These are found in the oviducal gland (spermatheca), where the large eggs are fertilized. The heart has an accessory chamber presumably providing extra blood flow to the long arms and large fins. The eyes are small open cups covered by a cornea but with no lens or iris. The rhabdomes are sometimes degenerate. The optic lobe is small with no granular layers of amacrine cells. The suboesophageal lobes are close together and the superior buccal lobe is attached to the brain, as in incirrate octopods. There is a large fin lobe. The peduncle lobe and basal lobes are large, in spite of the small eyes, indicating their importance for locomotion. There are no giant fibres. The supraoesophageal lobes are small, with development only of the tactile region (inferior frontal lobe) and reduction of the superior frontal and vertical lobe system. There are large epistellar bodies but no cranial photosensitive vesicles. The optic gland is clearly of neural origin. The statocysts are very large and typically octopodan with a single macula and one anticrista, but the crista is not subdivided. Cirrothauma, like other cirrates, thus shows some features that are present in Vampyroteuthis, and others that are found in decapods, as well as many present in the octopods without fins. These animals represent in some ways an early condition of the coleoid stock.