The Bryan-Cox primitive equation model is examined in terms of the stability of an ocean current by intercomparison with the other models, taking a focus on different representations (finite difference schemes) of continuous stratification: the Bryan-Cox level model, in which density is calculated at the same depth as horizontal velocity, versus the other level model with density calculated at the same depth as vertical velocity as well as a layer (isopycnal) model, in which vertical displacement of isopycnals represents density changes. Stability analyses are carried out for highly idealized cases: a basic flow with vertical shear only. The two-level models are first numerically examined for nongeostrophic cases, whose results are then confirmed with analytical solutions of the quasi-geostrophic versions. The analytical solutions are extended to the multi-level models. The instability of the basic current in the Bryan-Cox model is shown to be overestimated with low vertical resolution and sensitive to distribution of vertical shear among levels. As the vertical resolution becomes higher, the growth rate rapidly approaches that of the continuous model, while additional unstable modes appear at high wavenumbers (these modes are neutral in the other two models). These deficiencies are related to its representation of stratification in the Bryan-Cox model. It is suggested that the Bryan-Cox model should be carefully applied to a study of mesoscale processes. ¿ American Geophysical Union 1993