Cd(C(4)H(4)N(2))(H(2)O)(2)MoO(2)F(4) (C(4)H(4)N(2) = pyrazine, pyz) was synthesized via hydro(solvato)thermal methods and characterized by single-crystal X-ray diffraction methods (P3(2)()21, no. 154, Z = 3, a = 7.4328(7) A, c = 16.376(2) A). Both of the known M(pyz)(H(2)O)(2)MoO(2)F(4) (M = Zn, Cd) compounds are comprised of trans-M(pyz)(2)(OH(2))(2)F(2) and cis-MoO(2)F(4) octahedra that share fluoride vertices to form helical chains along the 3-fold screw axes. Individual chains are bridged to six symmetry-equivalent helices through metal-pyrazine and OH(2)...F and OH(2)...O hydrogen bonds. Structural comparisons of similar oxyfluoride chains demonstrate that they can be varied from linear to helical through (1) the replacement of pyridine or pyrazine by H(2)O molecules and (2) the substitution of cis-directing MoO(2)F(4)(2-) anions in place of trans-directing WO(2)F(4)(2-) or TiF(6)(2-) anions. Infrared absorption (IR) measurements for M = Cd show two distinct O-H stretches corresponding to hydrogen-bonded O-H...F and O-H...O groups. Contrastingly for M = Zn, IR measurements exhibit O-H stretches for averaged hydrogen-bonded O-H...(O/F) groups, free (unbound) O-H groups, and higher energy Mo-F stretches. The IR data suggest a small fraction of the O-H...F hydrogen bonds are broken in the M = Zn analogue as a result of the racemic twinning. Both compounds exhibit nonlinear optical behavior, with second harmonic generation (SHG) intensities, relative to SiO(2), of approximately 0.25 (<d(ijk)(2epsilon)> = 0.28 pm/V) for the racemically twinned Zn(pyz)(H(2)O)(2)MoO(2)F(4) and approximately 1.0 (<d(ijk)(2epsilon)> = 0.55 pm/V) for the enantiopure Cd(pyz)(H(2)O)(2)MoO(2)F(4).