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The elastic constants of the two orthorhombic crystals (NH4)2C2O4. H2O and (NH4)HC2O4.½H2O were determined by diffraction of light by ultrasonic waves. These constants and those of the triclinic (NH4)H3(C2O4)2.2H2O previously measured are correlated with the crystal structure. All three crystals show extreme elastic anisotropy which may be explained by the layer-like packing of the oxalate groups. The minimum elastic stiffness is observed normal to the C2O4 planes, whereas the direction of the maximum elastic stiffness may be correlated with the course of the periodic bond chains. It is shown that hydrogen bonds make a considerable contribution to the elastic properties of crystals. Correlations between elastic behaviour, morphology, and optical properties are discussed.