Neutral Higgs bosons of the Standard Model and of the MSSM are searched for in the data collected at a centre-of-mass energy of 188.6 GeV by the ALEPH experiment at LEP, with an integrated luminosity of 176 pb−1 . No evidence for a signal is found. A lower limit of 92.9 GeV/c2 at 95% confidence level is set on the mass of the Standard Model Higgs boson, with an expected sensitivity of 95.9 GeV/c2 . In the MSSM, for tanβ≥0.7 and for benchmark parameter choices, observed (expected) lower limits of 82.5 (83.1) GeV/c2 and 82.6 (83.2) GeV/c2 are derived for the masses of the neutral Higgs bosons h and A , respectively. An update of the general MSSM parameter scan is also presented.