The Na2 Rydberg states have been observed for 15 ^ n ^ 90 and 4 ^ / ^ 45. The evolution of the spectra is studied as a function of the relative values of oo e i, the electronic rotational frequency, and OJ N , the nuclear rotational frequency. The molecular eigenfunction is found to be pure Hund's case a when ka) e \ = 2a> N (k being an integer). This may be explained in terms of stroboscopic effects arising from the movement of the Rydberg electron relative to the ionic core.PACS numbers: 33.80.Eh, 33.10.-n In highly excited molecular Rydberg states, the rotational frequency w el of the Rydberg electron in its orbital motion can become smaller than the rotational frequency a) N of the nuclei. Under these conditions, the Born-Oppenheimer approximation is no longer valid and the electron angular momentum 1 tends to be decoupled from the internuclear axis.The interpretation of these effects was rather involved, 1 until the experimental work of Herzberg and Jungen 2 on H 2 whose interpretation by quantum-defect theory was due to Fano. 3 However, in their experiment they observed only Rydberg levels with n ^ 40 and / = 0,1,2.Recently optical-optical double resonance 4 " 8 has proved to be a powerful technique to study molecular Rydberg states. Using this method we have observed Na 2 molecular Rydberg states for 15^ n ^ 90 and 4 ^ / ^ 45. These new results enable us to study in detail the molecular spectrum when o) el = A transitions is explained by the mixing of wave functions, due to A doubling. 9 As n increases, rotational perturbations become important, and the regular structure of the spectrum is lost. For the interpretation of these spectra we have used the multichannel quantum-defect theory introduced by Seaton, 10 and applied to molecular Rydberg states by Fano. 3 The theoretical aspects a...