A combined high-resolution (6 meV) HeI photoelectron (PE) and ab initio theoretical study of the A (2)Sigma(+) ion system of HI and DI has been conducted to elucidate the origin of a peculiar "holelike" feature in the vibrational distribution found in the high-resolution (6 meV) threshold photoelectron (TPE) spectrum of HI. The PE and TPE spectra were found to yield essentially identical results. Ab initio potential energy curves for the low-lying cationic states of HI have been calculated for the first time with and without spin-orbit contributions included. It has been found that the diabatic A (2)Sigma(+) state of HI+ is strongly predissociated due to spin-orbit coupling with the (4)Sigma(-), (2)Sigma(-), and (4)Pi repulsive states leading to a complex set of adiabatic curves. It is shown that the adiabatic A (2)Sigma(1/2)(+) state is only slightly bound (by 260 cm-1 after suitable adjustments of the positions of the various repulsive potentials relative to that of the A state are made based on observed atomic spectral data) and should support at most one vibrational level in both HI+ and DI+. However, using the complex rotational method, it was possible to calculate the energies, predissociation linewidths, and rotational constants of a number of nonstationary vibrational levels (or resonances) of the A (2)Sigma(1/2)(+) state. Reasonably good agreement has been found between experiment and theory. The observed "hole" in the TPE and PE spectra is attributed to the fact that the stability of the v(+)=1 and 2 levels is notably less than for v(+)=0 in the A (2)Sigma(1/2)(+) state of both HI+ and DI+. (C) 2003 American Institute of Physics.