The bifurcation of two-dimensional internal solitary waves in a perfect density stratified fluid between horizontal walls under gravity is studied near to a point of incipient eddy formation. It is shown that eddies do not attach to the walls. Moreover, along the bifurcating branch there is always a flow with a singular cusped streamline before the formation of eddies. This flow with the cusped streamline is an example of what we call an internal wave of limiting form, by analogy with the Stokes wave of extreme form in the free surface problem. Two examples are given where the primary density stratification ensures the existence of a limiting wave of depression in one case, and of elevation in the other.