In two-parameter families of vector fields there can be curves in the
parameter plane along which orbits homoclinic to hyperbolic equilibria
occur. Such curves can end at a point where there is an orbit homocli
nic to an equilibrium undergoing saddle-node or transcritical bifurcat
ion. Convergence and stability results are presented for a method of a
pproximating these special parameter values and their associated homoc
linic orbits.