Seven monoclinic isotypic compounds with the general formula Na7M3(X2O7) 4 have been synthesized by crystallization in a flux of sodium phosphates or arsenates. They exhibit high ionic conductivity (sigma almost-equal-to 10(-3)-10(-2) OMEGA-1 cm-1 at 300-degrees-C) and good cation exchange properties particularly with Ag+ ions. At temperatures varying from -20-degrees-C to 240-degrees-C, depending on the particular compound, they undergo a reversible phase transition, alpha half arrow right over half arrow left beta, which is associated with a loss of long range ordering of the sodium ions and results in an increase of the conductivity. The crystal structures of beta-Na7Fe3 (AS2O7)4 and alpha-Na7Fe3(P2O7)4 have recently been determined and a model of sodium diffusion paths has been proposed. This model indicates a two-dimensional conduction within planes parallel to (001). Conductivity measurements performed on single crystals confirm this two-dimensional character with a sigma(parallel-to)/sigma(perpendicular-to) ratio of about 2 x 10(3).