A linear quasi-geostrophic model and a non-linear balanced model are used to study the properties of the oceanic baroclinic waves. From a linear point of view, the oceanic meso-scale (200-400 km) disturbances found near the Brazil and Falkland currents confluence zone seem to be generated by baroclinic instability. Non-geostrophic and non-linear effects due to a single original wave are superimposed on the linear fields associated with the most unstable wave. Characteristics very similar to observations are obtained in the evolution to finite amplitude. The evolution of oceanic thermal rings is very well reproduced by the non-linear model. However, the stage of saturation is not reached in the model results since the feedback to the thermal basic state is not included.