The production process of the charged Higgs-boson associated with a boson at electron-positron colliders is discussed in the two-Higgs-Doublet Model (2HDM) and in the Minimal Supersymmetric Standard Model (MSSM). The process is induced at one-loop level in these models. We examine how much the cross section can be enhanced by quark- and Higgs-loop effects. In the non-SUSY 2HDM, in addition to large top-bottom (-) loop effects for small (), the Higgs-loop diagrams can contribute to the cross section to some extent for moderate values. For larger $\tan \beta\gg \sqrt{m_t/m_b}$), such enhancement by the Higgs non-decoupling effects is bounded by the requirement for validity of perturbation theory. In the MSSM with heavy super-partner particles, only the - loops enhance the cross section while Higgs-loop effects are very small.

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