The quaternary hydrides (deuterides) SrGaGeH(D), BaGaSiH(D), BaGaGeH(D), and BaGaSnH(D) were obtained by investigating the hydrogenation behavior of AeGaE intermetallic compounds (Ae = Ca, Sr, Ba; E = Si, Ge, Sn), and structurally characterized by powder X-ray and neutron diffraction as well as solid state (1)H NMR investigations. The new main group metal/semimetal hydrides were found to crystallize with the simple trigonal SrAlSiH structure type (space group P3m1, Z = 1, a = 4.22-4.56 A, c = 4.97-5.30 A) and feature a two-dimensional polyanion [GaEH](2-) that corresponds to a corrugated hexagon layer built from three-bonded Ga and E atoms. H is terminally attached to Ga. In BaGaSiD, a considerable degree of stacking disorder could be detected. Polyanions [GaEH](2-) are electron precise, and the hydrides AeGaEH display small band gaps in the range of 0.1-0.6 eV at the Fermi level. This is in contrast to the metallic precursor phases AeGaE, which are representatives of the AlB2 structure type or variants of it. Hydrogenation has only minor consequences for the metal/semimetal atom arrangement, and the induced metal-nonmetal transition is reversible for SrGaGe, BaGaSi, and BaGaGe. BaGaSnH partially decomposes into a mixture of intermetallic compounds upon hydrogen release. Desorption temperatures are above 400 degrees C.