Ab initio calculations have been performed to investigate the nature of the low-lying electronic states and the rovibrational energy levels of the electronic ground state of HAlF+ and HAlCl+. The one-dimensional cuts of the low-lying states of both cations have been investigated at the complete active space self-consistent field level, revealing the single-configuration nature of the electronic ground states. Using explicitly correlated coupled-cluster methodology and core-valence basis sets, the three-dimensional potential energy surfaces of both species have then been generated, and the rovibrational energy levels were computed variationally. The analysis of the results reveals the similar nature of the Al-H bond in both species, according to their equilibrium bond lengths and to the Al-H stretching mode frequencies. The rovibrational energy levels of the deuterated isotopologues are also presented.