Searches for neutral Higgs bosons in the Standard Model and the MSSM have b
een performed using data collected by the DELPHI experiment at a centre-of-
mass energy of 188.7 GeV, corresponding to an integrated luminosity of 158
pb(-1). These analyses are used, in combination with our results from lower
energies, to set new 95% confidence level lower mass bounds on the Standar
d Model Higgs boson (94.6 GeV/c(2)) and on the lightest neutral scalar (82.
6 GeV/c(2)) and neutral pseudoscalar (84.1 GeV/c(2)) Higgs bosons in a repr
esentative scan of the MSSM parameters. The results are also interpreted in
the framework of a general two-Higgs doublet model.