Final results of the searches for neutral Higgs bosons in e+ e- collisions at s**(1/2) up to 209-GeV

The final results of the ALEPH search for the Standard Model Higgs boson at LEP, with data collected in the year 2000 at centre-of-mass energies up to 209 GeV, are presented. The changes with respect to the preceding publication are described and a complete study of systematic effects is reported. The findings of this final analysis confirm the preliminary results published in November 2000 shortly after the closing down of the LEP collider: a significant excess of events is observed, consistent with the production of a $115 \Gcs$ Standard Model Higgs boson. The final results of the searches for the neutral Higgs bosons of the MSSM are also reported, in terms of limits on $\mh$, $\mA$ and $\tanb$. Limits are also set on $\mh$ in the case of invisible decays. Comment: 15 pages, 6 figures