The nd (1)Delta(g) (n = 6, 7, and 8) Rydberg states of Na(2) correlating with the asymptotic limits of Na(3s) + Na(nd) have been observed using high-resolution cw optical-optical double resonance spectroscopy corresponding to the rovibrational transitions X (1)Sigma(g)(+)(v("),J(")) + h nu(pump) --> B (1)Pi(u)(v('),J(')) + h nu(probe) --> nd (1)Delta(g)(v,J). Totals of 104, 83, and 45 identified rovibrational e/f-parity levels in the ranges of v = 0-11, 11 < or = J < or = 83; v = 0-10, 11 < or = J < or = 83; and v = 0-10, 11 < or = J < or = 65, have been assigned to the 6d (1)Delta(g), 7d (1)Delta(g), and 8d (1)Delta(g) states, respectively. Using the observed quantum levels, molecular constants were determined from the Dunham fits of the e-parity levels and the Rydberg-Klein-Rees potential curves were constructed for the nd (1)Delta(g)(n = 6-8) states. The characteristics of the estimated Lambda-doubling splitting constants (q(0), q(v), and mu) with n(= 5-8) of the nd (1)Delta(g) series have been explored. Detailed investigations reveal that the nd (1)Delta(g)(n = 6-8) states involve L uncoupling from the internuclear axis and each of these states is affected by an asymmetric perturbation caused by the up and down adjacent states. The rotational-branch intensity and position anomalies in the observed spectra of the nd (1)Delta(g) series (n = 5-8) of Na(2) lead to the conclusion that due to the effects of the L-uncoupling perturbations, the same l complexes approaching the same ion-core limits result in the same l-mixing processes which lead to the formation of the supercomplexes due to the anisotropy of the molecular-ion [Na(2)(+)(3s)] field. This would open up opportunities to study the effects of L uncoupling and perturbations in the nd series and high Rydberg states of other alkali dimers.