Abstract. The zero-field conductivities (σ) of polycrystalline title materials, are governed by intergrain transport. In the majority of cases their σ(T) can be described by the "fluctuation induced tunnelling" model. Analysis of the results in terms of this model reveals two remarkable features: 1. For all Sr2FeMoO6 samples of various microstructures, the tunnelling constant (barrier width × inverse decay-length of the wave-function) is ~ 2, indicating the existence of an intrinsic insulating boundary layer with a well-defined electronic (and magnetic) structure. 2. The tunnelling constant for all cold-pressed samples decreases linearly with increasing magnetic-moment/formula-unit.