The nuclear quadrupole coupling and spin-rotation constants of aluminum in AlH and AlD have been determined using coupled cluster theory with single and double excitations as well as perturbative inclusion of triples [CCSD(T)] combined with large correlation-consistent basis sets, cc-pCVXZ (X = T, Q and 5) and aug-cc-pCVXZ (X = T, Q). The anharmonic vibrational frequencies have been computed using second-order vibrational perturbation theory and the effects of vibrational averaging on the hyperfine constants have been determined. The ground state dipole moment has been determined for both isotopologues (AlH and AlD) and shown to depend critically on vibrational averaging. For completeness, the isotropic and anisotropic nuclear magnetic shielding tensors are also reported. All the results agree well with the best available experimental measurements, and in some cases (spin-rotation constants and dipole moments) refine the known data. The present computational results for the vibrationally averaged electric field gradients suggest that the currently accepted nuclear quadruple moment for 27Al of 146.6 ±1.0 mb may be slightly underestimated. Based on the experimental measurements of the nuclear quadrupole coupling for AlH (AlD) and best computational determinations of the vibrationally averaged electric field gradients, the quadruple moment of 27Al is determined to be 149 ± 2 mb (148 ± 3 mb). However, this conclusion would be further strengthened with more precise experimental measurement of the 27Al nuclear quadrupole coupling for AlH and AlD.