The ionic conductivity of members of K(3-x)M(x)ZrF(7) (M=NH4, Tl and 0 less than or equal to x less than or equal to 3) solid solutions was investigated using complex impedance spectroscopy. Transient NMR measurements were carried out on F-19, H-1 and Tl-205 in order to specify the mobile species. The structure of KTl2ZrF7 has been refined from single crystal diffraction data. Correlations between all these experimental results allow to conclude that a long-range motion of the monovalent cations enhanced by the rotational/reorientational motion of the (ZrF7)(3-) complex anions is responsible for the ionic conductivity of these phases. Comparison of the ionic conductivities of Tl, NH4 and K compounds as well as that of some compositions among their solid solutions supports the conclusion that the higher performances of the pure thallium compound can be related to the high polarisability of this ion.