The Li1+xMxHf2-x(PO4)(3) (M = Cr, Fe, Bi) systems have been studied and single phases have been isolated for M = Cr and Fe. The samples have been characterized by X-ray powder diffraction, diffuse reflectance and impedance spectroscopy. There is a reconstructive transition between rombohedral NASICON and orthorhombic Sc-2(WO4)(3)-type structures as a function of x, at very low values, 0.2 and 0.1 for Cr and Fe, respectively. For the Cr series, a further subtle structural change has been observed for I values higher than 1.7. These phases have the Sc-2(WO4)(3)-type framework, but the symmetry is orthorhombic Pcnb at low values of x and monoclinic P2(1)/n at high values. The structural changes are discussed on the basis of the sizes of the cavities left by the two frameworks and the lithium order/disorder in these voids. These materials are ionic conductors and their electrical behaviours are also discussed.