Results of quantum and semiclassical calculations obtained for two different potential-energy surfaces are used to discuss spectroscopic properties and isotope effects of the linear IHI and IDI molecules. The potentials are a purely repulsive LEPS surface and a DIM-3C potential with two van der Waals type minima for equivalent IH ··· I and I ··· HI configurations. Both systems are dominated by the effect of vibrational bonding giving rise to some very unusual spectroscopic phenomena, which are discussed in detail. The different vibrational frequencies and rotational constants are roughly estimated as ν₁ = 120 (100) cm⁻¹, ν₂ = 280 (210) cm⁻¹, ν₃ = 360 (160) cm⁻¹ and B = 0.0194 (0.0196) cm⁻¹ for IHI (IDI). A detailed discussion of the dependence of ν₁, ν₂ and B on ν₃, their sensitivity to variations of the potential-energy surface, and a comparison with the vibrational frequencies of I₂ and HI (ID) is given. It is predicted that there exists only one excited level of the antisymmetric stretching mode. The numbers of symmetrical stretching and bending levels are fairly constant or may even decrease upon deuteration. Simultaneously deuteration destabilizes the molecule. These unusual phenomena are rationalized by our calculations. A set of criteria for observing infrared and Raman bound-to-bound and bound-to-resonance state transitions are presented for the IHI and IDI molecule.