Nonresonant excitation of H-2 at 248 nm using 5 ps and 0.5 ps laser pulses with intensities 5x10(11) and 5x10(12) W/cm(2), respectively, is studied by measurement of the angle-speed distributions of the H+ photofragment using velocity map imaging. Three main H+ production channels are observed: (a) three-photon dissociation to H(n=1)+H(n=2) followed by photoionization of H(n=2); (b) dissociative (auto)ionization following four-photon absorption to form H(n=1)+H++e(-); and (c) autoionization from a doubly excited state producing a H-2(+) vibrational distribution peaking at (upsilon (+)=2,7,13) and subsequent photodissociation of these vibrationally excited ions. In the neighborhood of the energy sum of three 248 nm photons lie transitions to the B-' (1)Sigma (+)(u)(3p sigma) vibrational continuum and the two bound states B-' (1)Sigma (+)(u)(4p sigma)(upsilon =2) and D (1)Pi (+)(u)(3p pi)(upsilon =4). These states are believed to play an important role in three-photon absorption and at the subsequent fourth photon level. Their effect on the observed kinetic energy and angular distributions is discussed.