State-to-state [X 1Σ+g(vi) → X 2Σ+g(vj)] and quasi state-specific [X 1Σ+g(vi, Ji) → X 2Σ+g(vj)] photon and electron-impact ionization cross sections of hydrogen and deuterium molecules have been obtained with a combined analysis of experimental measurement and theoretical calculations. Rotation state ionization transitions are considered using the p-partial wave approximation. Previously calculated photoionization transition moments are refined and extended to ∼300 eV using accurate experimental photoionization cross sections. The transition moments are used to obtain the photoionization cross sections and oscillator strengths for the H2 and D2 X 1Σ+g(vi, Ji) → H+2 and D+2 X 2Σ+g(vj, Jj) transitions. The calculated ionization oscillator strengths, together with excitation functions derived from electron-impact ionization measurements of H2, enable accurate determination of electron-impact ionization cross sections for both H2 and D2 transitions to (vj, Jj) levels of the X 2Σ+g state at energies ranging from threshold to the non-relativistic limit. The autoionizing singlet-ungerade states contribute at least 0.6–1% of the total e+H2 →H+2 cross section. The e+D2 →D+2 and e+H2 →H+2 cross sections are very similar above the threshold energy region. The D2 cross section is ∼1.6% larger than the H2 cross section. Thermally averaged nondissociative ionization cross sections of H2 and D2 at temperatures appropriate for plasma and planetary applications have been tabulated.