NdGa hydride and deuteride phases were prepared from high-quality NdGa samples and their structures characterized by powder and single-crystal X-ray diffraction and neutron powder diffraction. NdGa with the orthorhombic CrB-type structure absorbs hydrogen at hydrogen pressures ≤ 1 bar until reaching the composition NdGaH(D)_1.1, which maintains a CrB-type structure. At elevated hydrogen pressure additional hydrogen is absorbed and the maximum composition recovered under standard temperature and pressure conditions is NdGaH(D)_1.6 with the Cmcm LaGaH_1.66-type structure. This structure is a threefold superstructure with respect to the CrB-type structure. The hydrogen atoms are ordered and distributed on three fully occupied Wyckoff positions corresponding to tetrahedral (4c, 8g) and trigonal–bipyramidal (8g) voids in the parent structure. The threefold superstructure is maintained in the H-deficient phases NaGaH(D)_x until 1.6 ≥ x ≥ 1.2. At lower H concentrations, coinciding with the composition of the hydride obtained from hydrogenation at atmospheric pressure, the unit cell of the CrB-type structure is resumed. This phase can also display H deficiency, NdGaH(D)_y (1.1 ≥ y ≥ 0.9), with H(D) exclusively situated in partially empty tetrahedral voids. The phase boundary between the threefold superstructure (LaGaH_1.66 type) and the onefold structure (NdGaH_1.1 type) is estimated on the basis of phase–composition isotherms and neutron powder diffraction to be x = 1.15.