Two new quaternary mixed metal oxide materials--InVTe(2)O(8) and InVSe(2)O(8)--have been synthesized, as crystals and pure bulk powders by standard solid-state reactions using In(2)O(3), V(2)O(5), and TeO(2) (or SeO(2)) as reagents. The crystal structures of the reported materials were determined using single-crystal X-ray diffraction. InVTe(2)O(8) crystallizes in the monoclinic centrosymmetric space group P2(1)/n (No. 14), with unit-cell parameters of a = 7.8967(16) Å, b = 5.1388(10) Å, c = 16.711(3) Å, β = 94.22(3)°, and Z = 4, and InVSe(2)O(8) crystallizes in the noncentrosymmetric space group Pm (No. 6) with unit-cell parameters of a = 4.6348(9) Å, b = 6.9111(14) Å, c = 10.507(2) Å, β = 97.77(3)°, and Z = 2. While the centrosymmetric InVTe(2)O(8) shows a two-dimensional (2D) layered structure composed of InO(6) octahedra, VO(4) tetrahedra, and TeO(4) polyhedra, the noncentrosymmetric InVSe(2)O(8) exhibits a three-dimensional (3D) framework structure with distorted InO(6) octahedra, VO(5) square pyramids, and SeO(3) polyhedra. Powder second-harmonic generation (SHG) measurements on InVSe(2)O(8), using 1064-nm radiation, indicate that the material has a SHG efficiency ~30 times that of α-SiO(2). Additional SHG measurements reveal that the material is not phase-matchable (Type 1). Infrared, ultraviolet-visible light (UV-vis) diffuse reflectance, and thermogravimetric analyses for the two compounds are also presented, as are dipole moment calculations.