We have used fast neutral beam laser spectroscopy to investigate transitions in the near-infrared, from the metastable (a^{3} \Sigma_{u}^{+})state to predissociating levels of the electronic state (c^{3} \Sigma_{g}^{+})of (\mathrm{He}{2}). A number of transitions were not readily identified, while others were easily identified using the tables of M. L. Ginter (J. Chem. Phys. 42, 561-568, 1965). Predictions of the width and the position of lines were obtained using the potential for the (c^{3} \Sigma{g}^{+})state, and led to identification of most lines as transitions between (a^{3} \Sigma_{u}^{+})and (c^{3} \Sigma_{g}^{+})in highly rotationally excited states. In a number of transitions the fine structure could be resolved. For these lines, the fine structure of the lower state was measured by laser-radiofrequency double-resonance spectroscopy. This gave the finestructure splittings for the (N) values: 7,9 , and 11 in (v=2) of (a^{3} \Sigma_{u}^{+})and (N=25,27), and 29 in (v) (=0) of (a^{3} \Sigma_{u}^{+}), where the latter were identified by their fine-structure splittings. We discuss the possible upper state of the transitions from these highly excited rotational levels, and argue that the upper state must have predominantly (c^{3} \Sigma_{g}^{+})character, but must also include a significant admixture of the (b^{3} \mathrm{I}_{g}) state due to rotational coupling. The measured fine structure is described by an effective fine-structure Hamiltonian including the spin-spin parameter. (\lambda), and the spinrotation parameter, (\gamma). These parameters and their dependence on rotation, (N), and internuclear distance, (R), has been determined. (a) 1995 Academic Press, Inc.