The mechanisms underlying dissociative recombination of H-2(+), D-2(+) and HD+ have been a matter of considerable debate. Superexcited states belonging to two different categories, leading to the so-called direct and indirect processes, are usually considered. The direct process involves doubly excited repulsive Rydberg states, which, at lower energies, possess configurations (2p sigma (u))(n/lambda), forming Rydberg series converging upon the (2)Sigma (+)(u)(2p sigma (u)) ionic limit, or, at higher energies, have configurations (2p pi (u))(n/lambda), leading to series converging upon the (2)Pi (u)(2p pi (u)) ionic state. In the indirect process, vibrationally excited levels of singly excited bound Rydberg states with configurations (1s sigma (g))(n/lambda), which form Rydberg series converging upon the X (2)Sigma (+)(g)(1s sigma (g)) ionic threshold, are thought to play a key role. Experimental studies of dissociative recombination are fraught with difficulties. In this contribution we shall explore the uses and advantages of resonance-enhanced multiphoton ionization, either with kinetic-energy-resolved electron detection (termed laser photoelectron spectroscopy), or with mass-resolved ion detection, to investigate the role of these superexcited states. Experiments via the B (1)Sigma (+)(u) intermediate state were carried out on H-2 and D-2 with (3 + 1) one-colour laser photoelectron spectroscopy, and on H-2 with a (1+1') two-colour scheme employing ion detection. In our experiments, competition between direct molecular ionization, autoionization and (pre)disscsciation was apparent. Above the dissociation threshold at which atoms in the ground and n=3 excited states are formed, the formation of molecular ions and of excited n=2 fragments was virtually terminated, to be replaced by the generation of n=3 fragments, Our observations can be explained by invoking a mechanism, which so Far has not received much attention, namely the direct excitation of vibrational continua of singly excited Rydberg states.