Cephalopod statoliths are paired calcareous stones which lie in cavities, the statocysts, within the skull. They have a form which, though variable, shows promise as a source of criteria for taxonomic and evolutionary studies. As a preliminary to more detailed studies, Clarke (1978) published a description of the form of a generalized teuthoid statolith, coined nomenclature for the various parts and gave a very brief survey of variation of statoliths within the living Cephalopoda. This nomenclature was used in a detailed description of fossilized teuthoid statoliths by Clarke & Fitch (1979). Here, descriptions of the statoliths of the living species Berryteuthis magister (Berry, 1913), Gonatopsis borealis Sasaki, 1923, Gonatopsis (Boreoteuthis) makko Okutani & Nemoto, 1964 and Gonatus fabricii (Lichtenstein, 1818) are given and the fossil Berryteuthis species described in outline by Clarke & Fitch (1979) is compared with B. magister. A statistical analysis of measurements of the statoliths of these five species has been made and the results are presented. This forms the first part of a general description of teuthoid statoliths and similar studies on the Ommastrephidae and the Loliginidae are in preparation.