Interacting rovibrational levels of the F-1 Sigma(g)(+) and E(1) Sigma(g)(+) states of Li-6(2) have been excited via the optical-optical double-resonance process, (F,E)(1) Sigma(g)(+) <-- A(1) Sigma(u)(+) <-- X(1) Sigma(g)(+). The resulting fluorescence in the region 7000-11 000 cm(-1), which has been examined at high resolution with a Fourier transform spectrometer, was found to consist of transitions to very high levels of the A(1) Sigma(u)(+) state. These are only observed when there is an interaction between the F state level and an E state level above the shelf in the potential curve, and occur when either level is excited. Levels up to v = 84, similar to 2.5 cm(-1) below the dissociation limit, have been assigned and the data extend well into the long-range region, up to R similar to 51 Angstrom. An analysis of the data in this region has yielded the following long-range parameters for the A(1) Sigma(+) state: D-0 = 9214.68(5) cm(-1), D-e = 9352.27(5) cm(-1), C-3 = 3.580(10) X 10(5) cm(-1).Angstrom(3), C-6 = 1.0(2) X 10(7) cm(-1).Angstrom(6). Based on the results of the analysis of the A(1) Sigma(u)(+) state data, a value of D-e(X(1) Sigma(g)(+) = 8517.03(05) cm(-1) has been calculated for the dissociation energy of the ground state of Li-6(2). (C) 1996 Academic Press, Inc.