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We develop a method for calculation of dissociative electron attachment cross sections based on the Fano- Feshbach projection-operator approach. The coupling between the diabatic state and electron continuum is calculated with the inclusion of orthogonality scattering and long-range electron-molecule interaction. The dynamics of nuclear motion in the non-local complex potential is treated by semiclassical theory. We apply the theory to the calculation of dissociative attachment to the H2 and HF molecules. Our results for attachment to ground-state hydrogen molecules and the near-threshold vibrational enhancement of H2 are essentially the same as previous non-local results. However, the shape of the energy dependence of the cross section for attachment to vibrationally excited states of H2 is slightly different. The calculated value for the total attachment cross section to the ground state of HF is consistent with the little experimental data available; more definite conclusions are difficult because of the approximate nature of the experimental results. The results for the vibrational enhancement are in very good agreement with experiment.