Searches for neutral Higgs bosons in the Standard Model and the MSSM havebeen performed using data collected by the DELPHI experiment at acentre-of-mass energy of 188.7 GeV, corresponding toan integrated luminosity of 158~pb$^{-1}$.These analyses are used, in combination with our results from lowerenergies, to set new 95\% confidence level lower mass bounds on theStandard Model Higgs boson (94.6 GeV/$c^2$) and on the lightest neutralscalar (82.6 GeV/$c^2$) and neutral pseudoscalar (84.1 GeV/$c^2$) Higgsbosons in a representative scan of the MSSM parameters. The results are alsointerpreted in the framework of a general two-Higgs doublet model.

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