Detailed information on Ln-4f/ligand-2p covalence and on differences in covalence between tetravalent Ln compounds with oxygen and fluorine was derived from Ln-M-4,M-5 XANES and Ln-3d XPS spectra of BaLnO(3) and Cs(3)LnF(7) (Ln = Ce, Pr, Tb). We show that the fine structures of the multi-peaked spectra can be well reproduced by calculations based on the single-impurity Anderson model supplemented by intra-atomic multiplet interaction. In this way, discrepancies between experiment and theory in previous studies of LnO(2) compounds could be resolved, like the question of covalence, which we find to be weaker for Tb(IV) as compared to Ce(TV) and Pr(IV) compounds.