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)=189-209 GeV, corresponding to an integrated luminosity of approximately 600 pb-1. Charged Higgs bosons are assumed to be pair-produced and to decay into q qbar, tau nu or A W+-. 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 BR(H+- -> tau nu) + BR(H+- -> qq)=1, motivated by general 2HDM type II models, excluded areas on the [m(H+-), BR(H+- -> tau nu)] 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+- -> tau nu). A scan of the 2HDM type I model parameter space is performed and limits on the Higgs-boson masses m(H+-) and m(A) are presented for different choices of tan(beta).
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