We demonstrate that an integrable approximation to the hydrogen atom in ort
hogonal electric and magnetic fields has monodromy, a fundamental dynamical
property that makes a global definition of action-angle variables and of q
uantum numbers impossible. When the field strengths are sufficiently small,
we find our integrable approximation using a two step normalization proced
ure. One of dynamically invariant sets of the resulting integrable system i
s a doubly pinched torus whose existence proves the presence of monodromy.