Abstract A search is made for charged Higgs bosons predicted by Two-Higgs-Doublet extensions of the Standard Model (2HDM) using electron-positron collision data collected by the OPAL experiment at $\sqrt{s}=189\mbox{--}209\ \mbox{GeV}$ , corresponding to an integrated luminosity of approximately 600 pb−1. Charged Higgs bosons are assumed to be pair-produced and to decay into $\mathrm{q} \bar{\mathrm{q}}$ , τν τ or AW±. No signal is observed. Model-independent limits on the charged Higgs-boson production cross section are derived by combining these results with previous searches at lower energies. Under the assumption $\mathrm{BR} (\mathrm{H}^{\pm} \to \tau\nu_{\tau}) + \mathrm{BR} (\mathrm{H}^{\pm} \to \mathrm{q} \bar{\mathrm{q}}) = 1$ , motivated by general 2HDM type II models, excluded areas on the $[m_{\mathrm{H}^{\pm}} , \mathrm{BR} (\mathrm {H}^{\pm} \to \tau\nu_{\tau})]$ plane are presented and charged Higgs bosons are excluded up to a mass of 76.3 GeV at 95 % confidence level, independent of the branching ratio BR(H±→τν τ). A scan of the 2HDM type I model parameter space is performed and limits on the Higgs-boson masses $m_{\mathrm{H}^{\pm}}$ and m A are presented for different choices of tanβ.