We discuss complementarity of discovery reaches of heavier neutral Higgs bosons and charged Higgs bosons at the LHC and the International Linear Collider (ILC) in two Higgs doublet models (2HDMs). We perform a comprehensive analysis on their production and decay processes for all types of Yukawa interaction under the softly-broken discrete symmetry which is introduced to avoid flavour changing neutral currents, and we investigate parameter spaces of discovering additional Higgs bosons at the ILC beyond the LHC reach. We find that the 500 GeV run of the ILC with the integrated luminosity of 500 fb^{-1} shows an advantage for discovering the additional Higgs bosons in the region where the LHC cannot discover them with the integrated luminosity of 300 fb^{-1}. For the 1 TeV run of the ILC with the integrated luminosity of 1 ab^{-1}, production processes of an additional Higgs boson associated with the top quark can be useful as discovery channels in some parameter spaces where the LHC with the integrated luminosity of 3000 fb^{-1} cannot reach. It is emphasized that the complementary study at the LHC and the ILC is useful not only to survey additional Higgs bosons at the TeV scale, but also to discriminate types of Yukawa interaction in the 2HDM.
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