The hydrogenation behavior of the polar intermetallic systems AeE(2) (Ae = Ca, Sr, Ba; E = Al, Ga, In) has been investigated systematically and afforded the new hydrides SrGa2H2 and BaGa2H2. The structure of these hydrides was characterized by X-ray powder diffraction and neutron diffraction of the corresponding deuterides. Both compounds are isostructural to previously discovered SrAl2H2 (space group P (3) over bar ml, Z = 1, SrGa2H2/D-2: a = 4.4010(4)/4.3932(8) angstrom, c = 4.7109(4)/4.699(1) angstrom; BaGa2H2/D-2: a = 4.5334(6)/4.5286(5) angstrom, c = 4.9069(9)/4.8991 (9) angstrom). The three hydrides SrAl2H2, SrGa2H2, and BaGa2H2 decompose at around 300 degrees C at atmospheric pressure. First-principles electronic structure calculations reveal that H is unambiguously part of a two-dimensional polyanion [E2H2](2-) in which each E atom is tetrahedrally coordinated by three additional E atoms and H. The compounds AeE(2)H(2) are classified as polyanionic hydrides. The peculiar feature of polyanionic hydrides is the incorporation of H in a polymeric anion where it acts as a terminating ligand. Polyanionic hydrides provide unprecedented arrangements with both E-E and E-H bonds. The hydrogenation of AeE(2) to AeE(2)H(2) takes place at low reaction temperatures (around 200 degrees C), which suggests that the polyanion of the polar intermetallics ([E-2](2-)) is employed as precursor.