The reaction of N-(phosphonomethyl)piperidine and N,N'-bis(phosphonomethyl)bipiperidine with zirconium(IV) in hydrofluoric acid media led to the preparation of two new zirconium fluoride phosphonate derivatives with 1D and 2D structure, respectively. Their structures were solved ab initio from laboratory powder X-ray diffraction (PXRD) data. The monophosphonate derivative, with formula ZrF2(HF)(O3PCH2NC5H10), has a 1D structure (triclinic, space group P (1) over bar, a = 6.6484(3) angstrom, b = 7.1396(3) angstrom, c = 12.2320(6) angstrom, alpha = 77.932(4)degrees, beta = 87.031(6)degrees, gamma = 78.953(5)degrees, V = 557.22(4) angstrom(3), and Z = 2) made of inorganic chains constituted from the connection of zirconium octahedra and phosphorus tetrahedra with the piperidine groups bonded on their external part. The diphosphonate derivative, with formula Zr2F4(HF)(2)(O3PCH2)NC10H18N(CH2PO3), has a 2D structure (triclinic, space group P (1) over bar, a = 6.6243(3) angstrom, b = 7.2472(4) angstrom, c = 12.2550(7) angstrom, alpha = 102.879(4)degrees, beta = 100.29(1)degrees, gamma = 101.287(7)degrees, V = 547.03(4) angstrom(3), and Z = 1) composed of the packing of covalent layers whose structure may be ideally obtained by the joining of adjacent chains of the ID compound. In these hybrid layers, inorganic regions made of the connectivity of zirconium octahedra and phosphorus tetrahedra alternate with organic regions represented by the bipiperidine moieties. A section dedicated to vibrational spectroscopy analysis is also included, mainly devoted to clarify some issues not easily deducible on the basis of PXRD data and to describe the fluorine environment inside zirconium phosphonate structures.