High oxygen conductivities can be achieved in cation ordered LnxZrl-x=xO2-l/2x (Ln=Gd, Nd) solid solutions with pyrochlore (P) structure. High values of the pre-exponential factor σo are correlated with the degree of anion disorder in the 8b oxygen sublattice (neutron diffraction). The activation energy ΔH is lowered by cation ordering (F-P transition; effect of ) due to the occurence of a preferential diffusion path. Maximum oxygen conductivity is achieved in (1−x)Bi2O3−x Ln2O3 solid solutions with fluorite related δ-Bi2O3 structure for Ln=Er and x=0.20. Neutron diffraction measurements indicate the occurence of short range ordering in “Er-O units” with relative small interatomic distances at T < 820 K. This leads to an increased activation energy.