We have calculated the energy spectrum of a highly excited atom in parallel electric and magnetic fields. The eigenvalues were obtained by semiclassical quantization of action variables calculated from first-order classical perturbation theory. For the field strengths studied, the electron moves on a Kepler ellipse whose orbital parameters evolve slowly in time, and first-order perturbation theory reduces the problem to just one degree of freedom. Action variables were calculated from perturbation theory and the eigenvalues were obtained by semiclassical quantization of the action. The semiclassical analysis leads directly to a correlation diagram which connects the eigenstates of the Stark effect to those of the diamagnetic effect. A classification scheme for the eigenstates is proposed. Comparison with first-order degenerate quantum perturbation theory verifies the accuracy of the semiclassical treatment.