Using a novel many-body approach, we report lattice dynamical properties of UO2 and PuO2 and uncover various contributions to their thermal conductivities. Via calculated Grüneisen constants, we show that only longitudinal acoustic modes having large phonon group velocities are efficient heat carriers. Despite the fact that some optical modes also show their velocities which are extremely large, they do not participate in the heat transfer due to their unusual anharmonicity. Ways to improve thermal conductivity in these materials are discussed.Today's nuclear fuels are based on 235 U and 239 Pu elements where in a typical set-up, a nuclear reaction heats up a pellet made of either UO 2 or its mixture with PuO 2 and the heat is transformed to electrical energy. One of the major issues is to conduct the heat from a core of the pellet to its outer area which makes the evaluation of a high temperature thermal conductivity a key problem. Unfortunately, the thermal conductivity of UO 2 is very low and as a result, even a gradual increase of its value may lead to significant breakthrough in the performance of commercial nuclear reactors currently operating worldwide.In the present work, we argue that it is the unexpectedly large anharmonicity of optical modes that results in a very low thermal conductivity of modern nuclear fuels. Consider semiconducting UO 2 which is a main element of UOX fuel, or a blend of U and Pu oxides which is a major substance of MOX fuel. The heat from the core of the pellet in these insulating systems is carried by phonons which are known to be very inefficient heat conductors. This brings a whole set of complex problems such as causing fuel pellets to crack and degrade prematurely, necessitating replacement before the fuel has been depleted.Unfortunately, studying thermal conductivity In the present work we use a novel electronic structure method [13] capable of describing Mott insulating materials in order to address the structural properties and thermal conductivity of the modern nuclear fuels. Both UO 2 and PuO 2 are calculated using a combination of local density approximation (LDA) [12] and Dynamical Mean Field Theory (DMFT) [14][15] where relativistic 5f shells of Uranium and Plutonium atoms are treated by exact diagonalization of corresponding many-body Hamiltonians obtained by allowing a hybridization between the 5f -electrons and the nearest oxygen 2p orbitals.It is well known that a strong spin-orbit coupling of about 1eV present in actinides splits 14-fold degenerate f level onto f 5/2 and f 7/2 states. Group theoretical considerations assume that under cubic crystal symmetry, the f 5/2 6-fold degenerate level is further split onto Γ 8 quadruplet and Γ 7 doublet. In both UO 2 and PuO 2 , the Γ 8 level comes approximately 0.1eV below the Γ 7 state, and valence arguments make it occupied by two electrons for the case of UO 2 and fully occupied by four electrons for the case of PuO 2 . This sequence of the levels dictates the low temperature properties of these two materials: The UO ...