Rotationally resolved transitions of the 5f pi (3) Pi(g)<--4s sigma a (3)Sigma(u)(+) and 5f sigma (3) Sigma(g)(+)<--4s sigma a (3)Sigma(u)(+) systems of Ar-2 have been observed by laser excitation spectroscopy in a pulsed corona discharge. These systems were previously observed at lower resolution [D. J. Kane et al., J. Chem. Phys. 96, 6407 (1992)] with the system tentatively labeled nl lambda Pi(g)-a and subsequently assigned as 5f pi (3) Pi(g)-a on the basis of theoretical considerations [P. Duplaa and F. Spiegelmann, J. Chem. Phys. 105, 1500 (1996)]. Rotational analyses for the (0-0) and (0-1) bands of both systems rue presented and the upper states characterized. The (0-2) bands of the 5f pi-a and 5f sigma-a transitions are observed also, as are the (0-0) band of 4f delta (3) Delta(g)-a (3) Sigma(u)(+) and the (1-0) and (2-0) bands of 5f pi-a, but with rotational structures insufficiently developed to permit analysis. The linewidths of the rotational lines of the above bands are much broader than are the lines of the 7p sigma (3) Sigma(u)(+)-a system previously analyzed [C. M. Herring et al., J. Chem. Phys. 101, 4561 (1994)], presumably because of increased lifetime broadening. Several spectral features observed in the 5f pi (3) Pi(g) band structures that are not apparently compatible with this upper state assignment are discussed.