The author considers two-parameter families of vector fields possessing a homoclinic orbit along a path in the parameter plane. These homoclinic orbits are homoclinic to a hyperbolic singularity that has a one-dimensional unstable manifold. The weakest stable and unstable eigenvalues of the linearized vector field at the singularity are supposed to be real. Given conditions on the vector field at begin and endpoint of the path of homoclinic orbits, conditions are found that ensure that somewhere along this path a homoclinic doubling occurs. The method used is Conley index theory, and thus verification of some nondegeneracy assumptions used in bifurcation theory is avoided.