The EPR-line shape of rare earth (RE) adsorbates at coverages low enough to ignore adatom-adatom interactions is studied theoretically. We analyse the conduction electron-local moment (k-f) interaction. The adatomic 5d states are hybridized with the conduction electrons and form a virtual bound state (VBS). The intra-atomic 5d-4f electron interaction transfers the finite 5d-VBS lifetime to the f shell. Covalent mixing and the atomic exchange interaction contribute directly to the k-f interaction. The anisotropic 5d-VBS charge distribution adds a crystal-electric field (CEF) effect to the 4f electrons which is comparable to that produced by the point charges. The eigenvectors of the Hund's-rule 4f-ground state in the presence of the combined CEF define the local g-tensor of the adsorbate.