In order to study the gerade Rydberg states of the rare-gas excimers the absorption spectra of Ne2 and Kr2 in the 3 Sigma u state were investigated. Using a dye laser a resolution of better than 1 cm-1 was achieved. The observed absorption bands were attributed to transitions to Ne2(3p, 3 Pi g), Ne2(4p, 3 Sigma g), Ne2(4p, 3 Pi g), Kr2(6p, 3 Sigma g), Kr2(6p, 3 Pi g), Kr2(7p, 3 Sigma g) and Kr2(7p, 3 Pi g) respectively. Although perturbations by crossings with repulsive curves are present, for most levels several vibrational transitions were identified and the spectroscopic properties are determined.