Probing the CP properties of the Higgs sector at ILC.

The violation of CP symmetry is one of Sakharov's conditions for the matter-antimatter asymmetry of the Universe. Currently known sources of CP violation in the quark and neutrino sectors are insufficient to account for this. Is CP also violated in the Higgs sector? Could the SM-like Higgs boson be a mixture of even and odd CP states of an extended Higgs sector? With what precision could such effects be measured at future electron-positron colliders? These questions will be discussed in the light of the latest and ongoing studies at ILC.