Electron impact ionization cross sections measured close to threshold are reported for both the monomers and dimers of ozone and OClO using a new high resolution electron impact apparatus. The present appearance energies AE(O-3(+)/O-3)=12.70 +/-0.02 eV, AE (OClO+/OClO)=10.55 +/-0.02 and AE(ClO+/OClO=13.37 +/-0.03 eV derived from the measured ionization cross sections are in excellent agreement with the vertical threshold values determined for these ions by high resolution PES and PIMS photoionization studies. The corresponding appearance energies determined for the dimer ions, 10.10 +/-0.3 eV for (O-3)(2)(+) and 9.87 +/-0.2 eV for (OClO)(2)(+), are both red shifted with respect to the monomer case. The bond energy (0.70-0.3+0.5) eV of (OClO)(2)(+) estimated from these data is similar to that of other dimer ions, whereas the bond energy of (O-3-O-3(+)) with (2.55-0.4+0.6) eV is rather large suggesting an unusual structure for the cationic ozone dimer ion. Based on quantum chemical calculations on various levels we are led to the conclusion that the ion produced by ionization of the ozone dimer is no longer a conventional dimer ion where the two monomer units are still present (as is the case for the OClO system), but rather an ion of form O-2.O-4(+) or a twisted ring structure of (O-6)(+).