The new ternary nitrides SrZrN2 and SrHfN2 have been synthesized by the solid state reactions of Sr2N with ZrN and HfN and characterized by powder X-ray diffraction. Both nitrides form structures in the hexagonal space group R(3) over barm$ (SrZrN2, a = 3.37302(5) Angstrom, c = 17.6756(3) Angstrom, Z = 3; SrHfN2, a = 3.34481(3) Angstrom, c = 17.6779(2) Angstrom , z = 3) and are isostructural with alpha-NaFeO2. The structures are constructed of alternating layers of strontium-nitrogen edge-sharing octahedra and either zirconium-nitrogen or hafnium-nitrogen edge-sharing octahedra stacked along the c axis. Alternatively, Sr2+ can be regarded as occupying octahedral holes between Zr(Hf)N-2 octahedral layers. The title nitrides are essentially diamagnetic at room temperature, consistent with the chemical composition. These compounds are the first alkaline earth ternary nitrides observed to have the alpha-NaFeO2 layered structure.