Anisotropy of electrical and dielectric properties, self-diffusion of K+ ions, and phase transitions in stoichiometric disordered K5B1-xRx(MoO4)(4) (R=Nd, Gd; x=0, 0.92, 1) single crystals are studied. A high value of the 2-D ionic conductivity by K+ ions (10(-3) S/cm, at 495 degrees C) is found in all samples. The fast ionic transport is parallel to the double layers formed by MoO4 tetrahedra. (c) 2005 Elsevier B.V. All rights reserved.