The electronic structure of Tm and Sm monochalcogenides, SmB 6 and Yb 4 As 3 is theoretically investigated from the first principles, using the fully relativistic Dirac LMTO band structure method. The electronic structure is obtained using the local spin-density approximation (LSDA), as well as the so-called LSDA+U approach. While the standard LSDA approach is incapable of correctly describing the electronic structure of such materials due to the strong on-site Coulomb repulsion, the LSDA+U approach is remarkably accurate in providing a detailed agreement with experiment for a number of properties.