  Searches for the neutral Higgs bosons h0 and A0, are used to obtain limits on
the Type II Two Higgs Doublet Model (2HDM(II)) with no CP-violation in the
Higgs sector and no additional particles besides the five Higgs bosons. The
analysis combines approximately 170 pb-1 of data collected with the OPAL
detector at sqrt{s} ~ 189 GeV with previous runs at sqrt{s} ~ mZ and sqrt{s} ~
183 GeV. The searches are sensitive to the h0, A0 -> qq, gg, tau+tau- and h0 ->
A0A0 decay modes of the Higgs bosons. For the first time, the 2HDM(II)
parameter space is explored in a detailed scan, and new flavour independent
analyses are applied to examine regions in which the neutral Higgs bosons decay
predominantly into light quarks or gluons. Model-independent limits are also
given.
