A two-layer Gulf Stream model is considered. We assume no motion in the lower layer and a basic state zonal jet in the upper. The purpose of the study is to examine numerically the validity of hydrodynamic stability investigations of the Gulf Stream. It is found that the ageostrophic influence depends on the basic state velocity profile and on the inverse radius of deformation, γ. In the case of a basic velocity profile without countercurrent, an increase in the Rossby number results in a more stable flow. When a countercurrent is included, the results depend on the radius of deformation and wavelength. For a realistic value of γ, short zonal waves are destabilized while long ones are stabilized. It is also found that an increase in γ stabilizes the flow for both profiles.