  When superimposing the potentials of external fields on the Coulomb potential
of the hydrogen atom a saddle point appears, which is called the Stark saddle
point. For energies slightly above the saddle point energy one can find
classical orbits, which are located in the vicinity of this point. We follow
those so-called quasi-Penning orbits to high energies and field strengths
observing structural changes and uncovering their bifurcation behavior. By
plotting the stability behavior of those orbits against energy and field
strength the appearance of a stability apex is reported. A cusp bifurcation,
located in the vicinity of the apex, will be investigated in detail. In this
cusp bifurcation another orbit of similar shape is found, which becomes
completely stable in the observed region of positive energy, i.e., in a region
of parameter space, where the Kepler-like orbits located around the nucleus are
already unstable. By quantum-mechanically exact calculations we prove the
existence of signatures in quantum spectra belonging to those orbits. Husimi
distributions are used to compare quantum-Poincar\'e sections with the
extension of the classical torus structure around the orbits. Since periodic
orbit theory predicts that each classical periodic orbit contributes an
oscillating term to photoabsorption spectra, we finally give an estimation for
future experiments, which could verify the existence of the stable orbits.
