The Doppler-free spectrum and the Zeeman effect of the A B-1(1u)(v(4)=1:b(1u))<--X (1)A(g)(v=0) transition of naphthalene in the 33 576.4-33 578.0 cm(-1) range has been measured by means of two-photon absorption spectroscopy with counter propagating light beams of identical wavelength within an external cavity. Rotational lines were fully resolved, and 1098 (Q(K))Q(J) lines of J=0-42, K=0-24 were assigned. The molecular constants of the A B-1(1u)(v(4)=1:b(1u)) state were determined. Deviations from the line positions calculated using the molecular constants were observed for several lines. Perturbations were not observed for K=0 but were observed to increase with increasing K. The perturbations were therefore identified as originating from a parallel Coriolis interaction. The Zeeman splittings for lines of a given J were observed to be maximum at K=0 and to decrease with increasing K. Analysis of these results indicate that the magnetic moment lies along the c axis (perpendicular to the molecular plane). Any lines broader than our instrumental resolution (5 MHz) were not observed at H=0 T. The J and K dependence of the Zeeman splittings of the A B-1(1u)(v(4)=1:b(1u))<--X (1)A(g)(v=0) transitions were observed to be regular. This observation and the small number of perturbed lines, leads to the conclusion that the resonance interaction of the A B-1(1u) state with the T-1 B-3(3u) and T-2 B-3(1u) states are small and negligible in the observed region.