Density functional (DF) electronic structure calculations for UFeX (X=Si, Ge) compounds were performed using fully relativistic optimized linear combination of atomic orbitals (OLCAO), relativistic general potential linear augmented plane wave (LAPW) and scalar relativistic augmented sphere wave (ASW) methods. The 5f-states of uranium were assumed itinerant and treated as band states. We confirm the experimental observation that UFeGe is a paramagnet. On the other hand, our extensive DF calculations including the fixed-spin-moment method predict an instability of the paramagnetic state of UFeSi in the orthorhombic TiNiSi structure. Since both UFeSi and UFeGe are isoelectronic with respect to the number of valence electrons the actual ground states result from a subtle interplay between the band filling of the free electron background (s-, p-, and U-d electrons) and the iron bonding bands on one side and the covalency (hybridization) between bonding predominantly 3d states of iron and antibonding predominantly 5f-states of uranium on the other side.