The vibrationally and rotationally specific cross section is investigated for the dissociative recombination (DR) of H + 2 and HeH + using the multi-channel quantum defect theory. In order to give the zero energy cross section, a convolution formula is introduced. A systematics in the vibrational dependence of DR is made clear. The rotational motion plays an important role in the DR at energies lower than 0.1 eV, causing large enhancement in some cases and rotational sensitivity. The

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... fic investigation indicates a possibility of a non-thermal distribution of the initial rotational states in storage-ring experiments on HD + .