Molecular dynamics (MD) simulations were performed to determine thermal expansion, thermal conductivity and diffusional properties of Th1-xNpxO2 and U1-xNpxO2 mixed oxides (MOX). The linear thermal expansion coefficient (LTEC) of Th1-xNpxO2 MOX increases with NpO2 concentration, while that of U1-xNpxO2 MOX decreases. The degradation of thermal conductivity in U1-xNpxO2 is predicted to be far less significant compared to Th1-xNpxO2 because defect-phonon scattering is less pronounced in U1-xNpxO2. Addition of 6.25 atom% NpO2 in ThO2 degrades the thermal-conductivity of ThO2 by 24.0–12.5% in the 750–1000 K temperature range whereas up to 50 atom% NpO2 doping in UO2 degrades the thermal-conductivity only by 13–2.3%. Analytical expressions have been derived that describe the predicted lattice parameters and thermal conductivities over the full temperature and compositional ranges. Oxygen diffusivity is higher in UO2 and NpO2 compared to ThO2. With the addition of Th4+ or U4+ to NpO2, the diffusivity decreases due to the increase in the migration barriers caused by the larger ionic radius of Th4+ or U4+. The addition of Np4+ to ThO2 or UO2 decreases oxygen diffusion due to the preference for the oxygen vacancy to be adjacent to Np4+, even though the migration barriers decrease due to the smaller size of Np4+. Our MD calculated binding energies of the oxygen vacancy can be correlated with the isolated oxygen Frenkel pair defect energies (O-FPisolated) of individual actinide oxides calculated using same interatomic potential set. Moreover, MD calculated oxygen vacancy binding energy is consistent with that calculated using density functional theory.