The solid-state syntheses, crystal structures, and characterization of two stoichiometrically similar quaternary mixed metal selenite and tellurite, In2Zn(Seo(3))(4) and Ga2Zn(TeO3)(4), respectively, are reported. While In2Zn(Seo(3)), crystallizes in the centrosymmetric monoclinic space group P-21/n (No. 14) with a = 8.4331(7) angstrom, b = 4.7819(4) angstrom, c = 14.6583(13) angstrom, and beta = 101.684(6)degrees, Ga2Zn(TeO3)(4) crystallizes in the non-centrosymmetric space group i-43d (No. 220) with a = b = c = 10.5794(8) angstrom. In2Zn(SeO3)(4) exhibits a two-dimensional crystal structure consisting of distorted InO6 octahedra, ZnO6 octahedra, and SeO3 polyhedra. Ga2Zn(TeO3)(4) shows a three-dimensional framework structure that is composed of GaO4 or ZnO, and TeO3 polyhedra. An effect of the framework flexibility on the space group centricity is discussed. The SHG (second harmonic generation) efficiency of noncentrosymmetric Ga2Zn(TeO3)(4), using 1064 nm radiation, is similar to that of KH2PO4 (KDP) and is not phase-matchable (Type 1). Complete characterizations including infrared spectroscopy and thermal analyses for the reported materials are also presented, as are dipole moment calculations.