The experimental electron density rho(r) of the two isomorphic salts KMnO(4) and KClO(4) was determined by a multipole analysis of accurate X-ray diffraction data at 120 K. The quantum theory of atoms in molecules was applied to rho(r) and to its Laplacian nabla(2)rho(r). The bonds were characterized using the topological parameters at the bond critical points of the density rho(r), nabla(2)rho(r), G(r) (kinetic energy density), V(r) (potential energy density) and H(r) (total energy density). According to the classification recently proposed by Espinosa, Alkorta, Elguero & Molins [J. Chem. Phys. (2002), 117, 5529-5542], the K-O and Cl-O bonds have a pure ionic and covalent character, respectively, while the Mn-O bonds show an intermediate behaviour. The results of the topological analysis of the experimental and theoretical (fully periodic Hartree-Fock and density functional calculations) electron density are in good agreement, even on a quantitative level. The atomic charges, determined by performing an integration over the topological basins, are about +2 e for Mn and Cl atoms. The ionic radius, estimated with the distance of the bond critical point from the nucleus, is in agreement with a charge of +2 e for the Mn atom.