Abstract The salient features of low-frequency current fluctuations, obtained from an analysis of eight current meter records from the continental shelf and slope of the southern Weddell Sea, are compared to baroclinic and barotropic theories. A simple baroclinic theory of internal waves is used successfully to predict high-frequency spectral cutoff values from low-frequency velocity ellipse calculations made from the continental slope mooring data. The success of this theory indicates that the higher spectral energy levels observed over the slope compared to the shelf are probably due to baroclinic motions. A barotropic model of free continental shelf waves probably by Saint-Guily (1976) is adapted for the local topography and the predictions of the model compared to observations. Coherences and phases between moorings separated by 10 and 160 km in the along-shelf direction provide substantial evidence of the existence of shelf waves as predicted by the theory for periods of 3–60 days and for the lowest ...