The nonlinear behaviour of the Kelvin-Helmholtz instability is investigated with a two-fluid simulation code in both sub-magnetosonic and super-magnetosonic regimes in a two-dimensional configuration chosen so as to represent typical conditions observed at the Earth's magnetopause flanks. It is shown that in super-magnetosonic regimes the plasma density inside the vortices produced by the development of the Kelvin-Helmholtz instability is approximately uniform, making the plasma inside the vortices effectively stable against the onset of secondary instabilities. However, the relative motion of the vortices relative to the plasma flow can cause the formation of shock structures. It is shown that in the region where the shocks are attached to the vortex boundaries the plasma conditions change rapidly and develop large gradients that allow for the onset of secondary instabilities not observed in sub-magnetosonic regimes.