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 sqrts=189-209 GeV, corresponding to an integrated luminosity of approximately 600pb-1. Charged Higgs bosons are assumed to be pair-produced and to decay into qq, tnt or AWpm. 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. Excluded areas on the [mHpm, BR(Hpm->TV)] plane are presented assuming BR(Hpm->tnt)+BR(Hpm->qq)=1. Under the above assumption, motivated by general 2HDM type II models, charged Higgs bosons are excluded up to a mass of 76.6GeV at 95% confidence level, independent of the branching ratio BR(Hpm->tnt). A scan of the 2HDM type I model parameter space is performed and limits on the Higgs-boson masses mHpm and mA are presented for different choices of tanb.

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