New results on oxygen self-diffusion (D*), surface exchange coefficient (k) and activation energy (E(a)) of oxygen self-diffusion for chosen compositions of manganite and cobaltite perovskites illustrate the effect of doping in the A and B sites of the ABO3 structure. The electrical conductivity (sigma(T)) was measured for the manganite group and permeability (J) was determined for the cobaltite perovskites. D* increases with increasing x in La1-x(Sr,Ca)x(Mn,Co)O3-delta due to formation of new oxygen vacancies by introducing metals of lower valency (M2+) into the A3+ sites. A substitution of M2+ for B3+ or a reduction of the metal in the B3+ site to a lower positive valency also increases D*. D* of the cobaltites is significantly higher than that of the manganites (by 4-6 orders of magnitude), however, the potentially high oxygen fluxes that would be allowed through the materials by the high D* values seem to be limited by the surface exchange kinetics. E(a)-values of the manganites are considerably higher than those of the cobaltites. In general, the electrical conductivity, sigma(T), decreased on doping the B site of the manganites with Co and Ni. However, whilst the pure manganite material exhibits a metallic type of conduction (i.e. sigma(T) decreased with increasing T), the conduction mechanism in the Co-doped and Ni-doped manganites changed to a localized hopping of charge carriers between the Mn3+ and Mn4+ sites (sigma(T) increases with increasing T).