Searches fur the neutral Higgs bosons predicted by the Standard Model (SM)
and the Minimal Supersymmetric extension of the Standard Model (MSSM) have
been performed with the OPAL detector at LEP. Approximately 170 pb(-1) of e
(+)e(-) collision data collected at root s approximate to 189 GeV were used
to search for Higgs boson production in the SM processes e+e- --> H(0)Z(0)
and the MSSM processes e(+)e(-) --> h(0)Z(0) and e(+)e(-) --> A(0)h(0). Th
e searches are sensitive to the <b(b)over bar> and tau(+)tau(-) decay modes
of the Higgs bosons, and also to the MSSM decay mode h(0) --> A(0)A(0). OP
AL search results at lower centre-of-mass energies have been incorporated i
n the limits, which are valid at the 95% confidence level. For the SM Higgs
boson, a lower mass bound of 91.0 GeV is obtained. In the MSSM, the limits
are m(H) > 74.8 GeV and m(A) > 76.5 GeV, assuming tan beta > 1, that the m
ixing of the scalar top quarks is either zero or maximal, and that the soft
SUSY-breaking masses are 1 TeV. For the case of zero scalar top mixing, th
e values of tan beta between 0.72 and 2.19 are excluded.