—Adults. Eight circum-oral arms, tentacles absent. Velar filaments absent; fins, when present, paddle-like, subterminal and widely separated. The shell is vestige and, when present, well developed and single, or reduced and paired. Arm cirri present or absent; arms with suckers in one or in two rows; suckers stalked or sessile, without horny rings. Eye lenses covered with primary and secondary transparent lids (cornea). Branchial canal generally present on gills between down-folded filaments. Radula present, reduced, vestigial, or absent; dentition homodont, heterodont, or ctenodont. Buccal membrane absent. Olfactory organ is a ciliated pit. Chromatophores present and functional (with muscles), or absent. (After Hochberg et al., in Sweeney et al., 1992).
Subdivided into the suborder Cirrata and the suborder Incirrata.
— Cirrata, or finned octopuses: gelatinous animals dotted with cirri on the arms and with a pair of fins and a large web; they are usually deepwater animals and rarely captured.
— Incirrata, or true octopuses comprises nine families, of which seven are European.
The following species of this order occur in, or nearby the North Sea; generally it are benthic species. Species marked with p have a pelagic juvenile stage and are keyed out both as adult and juvenile; the non-marked species have (probably) a benthic juvenile stage.
p Cirroteuthis muelleri Eschricht, 1838
p Haliphron atlanticus Steenstrup, 1861
p Eledone cirrhosa (de Lamarck, 1798)
p Octopus vulgaris Cuvier, 1797
Graneledone verrucosa (Verrill, 1881)
Eledone cirrhosa (de Lamarck, 1798)
Bathypolypus arcticus Prosch, 1849
Bathypolypus bairdii (Verrill, 1881)