Neutral Higgs bosons of the Standard Model and of the \MSSM\ aresearched for in the data collected at a centre-of-mass energy of \cme\,\G\ by the \ALEPH\ experiment at \LEP, with an integrated luminosity of \lumabs\,\invpb. No evidence for a signal is found.A lower limit of \lhSMobs\,\Gcs\ at 95\%~confidence level is set on the mass of the Standard Model Higgs boson.In the \MSSM, for \tanb \ge 0.7 and for benchmark parameter choices, lower limits of \lhobs\,\Gcs\ and 82.6\,\Gcs\ are derived for the masses of the neutral Higgs bosons \h\ and \A, respectively.An update of the general \MSSM\ parameter scan is alsopresented.

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