Herzberg has recently observed an absorption band system and dissociation continuum in HD analogous to the H 2 system B′ 1 Σ u + ← X 1 Σ g + . Two absorption edges, separated by 21.5 ± 0.3 cm −1, are seen at the low-frequency limit of the dissociation continuum; the intensity of absorption above the upper edge is roughly twice that between the two edges. The observed edge splitting is some-what less than the term value difference between [ D(1s) + H ∗(2s, 2p) ] and [ D ∗(2s, 2p) + H(1s) ] of 22.37 cm −1. In addition, an intense, line-like feature is observed at 14.5 cm −1 above the lower edge. Absorption edge doubling can be quantitatively described by the two-channel scattering theory developed in this paper. The electronic transition involved is assumed to be the same as that of H 2. Computations using potential curve data for the B′ 1 Σ u + state of H 2 and simple parametric forms for the exciton splitting between this state and a corresponding 1 Σ g + state reproduce not only the basic two-edge structure observed, but also predict the existence of a resonance in the photoabsorption cross section at the position observed. The general structure of edge-doubling absorption profiles and their dependence on system parameters has been investigated using analytically solvable models. It is found that a narrow interthreshold feature like that observed in HD can occur only under certain very precise “tuning” conditions, requiring a coincidence of a virtual bound level resonance of the B′ 1 Σ u + state with a similar level resonance of the 1 Σ g + state. The computations using H 2 potentials verify the sensitivity of this tuning. The narrow resonance in HD is therefore evidence that the (unknown) ( E′) 1 Σ g + potential is attractive, but assignments v′ g′ , v u ′ for the coincident level pair cannot be made without information from the discrete HD spectrum. The model studies also show that when an upper absorption edge occurs it is always located at the upper threshold, but in certain cases the lower edge may appear shifted upward from threshold and slightly broadened. Assuming this effect is the explanation of the ∼1 cm −1 edge-splitting discrepancy, we conclude that the upper edge provides the more accurate datum for the HD dissociation energy.