The bonding in hypohalous acids has been investigated from the topological analysis of the electron localization function (ELF) at the Becke3LYP and Hartree-Fock levels. The interaction between halogen and oxygen atoms has been characterized by the presence of bonding, disynaptic attractors V(O,X) X=F, Cl, Br, and I with the mean electron population (N) over bar of 0.32, 0.61, 0.35e, and 0.35e, respectively. In the case of HOBr, the possibility of a strong contribution of 3d bromine core electrons to the valence shell has been observed. On the base of the bonding evolution theory (BET), the O-F bond has been recognized as a covalent, polarized one whereas, the bonding between O and Cl, Br, and I atoms is of the electron donor-acceptor-type with halogen donating the electron density to valence shell of oxygen. The observed difference between HO+F-and HO-X+ (X=Cl, Br, and I) polarizations is reflected in topology of ELF maps with a large localization domain surrounding the V(F) and V(F,O) attractors in HOF and a common superbasin encompassing the V(O,H), V(O), and V(X,O) attractors in HOCl, HOBr, and HOI. The very large values of the relative quantum fluctuation (lambda), above 0.8, found for V(O,X) suggest that the covalent electron density is almost entirely delocalized over other basins. The comparison of the mean electron population ((N) over bar) of the V(H,X) and V(H,O) basins computed for hydrohalic (HX) and hypohalous acids (HOX) has revealed that the population alters in line with values of Delta E-acid, therefore can be used as a approximate measure of acidic properties of molecules. The topological analysis of the ELF function supports the concept of probonded electronegativity and its usefulness as a tool for prediction of the nature of the oxygen-halogen linkage.