We have performed a detailed analysis of the magnetic (collinear and non-collinear) order and the atomic and electron structures of UO₂, PuO₂ and UN on the basis of density functional theory with the Hubbard electron correlation correction (DFT + U). We have shown that the 3-k magnetic structure of UO₂ is the lowest in energy for the Hubbard parameter value of U = 4.6 eV (and J = 0.5 eV) consistent with experiments when Dudarev's formalism is used. In contrast to UO₂, UN and PuO₂ show no trend for a distortion towards rhombohedral structure and, thus, no complex 3-k magnetic structure is to be anticipated in these materials.