An overview is given of several concepts that are useful when dealing with numerical BVP. In particular a generalisation of the well-conditioning concept for nonlinear problems is considered. This is done to be able to investigate a class of second order scalar nonlinear problems. A detailed study of the solution structure is made for this class. The results are applied to two specific problems (Korteweg-de Vries and Burgers) and a way is indicated to stabilize these (ill-posed) BVP.