Nonadiabatic quantum scattering calculations have been carried out for the reactive and nonreactive quenching of OH(A(2)E(+)) in collisions with molecular H-2 on two new potential energy surfaces of the 1A' and 2A' states. Integral cross sections of the reactive and nonreactive quenching channels and the quantum state distributions of the nonreactive channel have been obtained. The theory reveals a high degree of rotational excitation of the quenched OH((XII)-I-2) products and vibrational excitation of the H-2 products. The calculated results are in good agreement with the existing experimental data. The topography of the potential energy surfaces in the conical intersection regions is provided in order to discuss the origin of the internal excitations of nonreactive products and the branching of the reactive and nonreactive channels.