We present the results on the searches for the SM and the MSSM
Higgs boson production in proton-antiproton collisions at s**(1/2) = 1.96 GeV
with the CDF detector.  The Higgs bosons are searched for in various
production and decay channels, with data samples corresponding to 400 pb-1.
Using these measurements, we set an upper limit on the production cross
section times branching fraction for the Standard Model Higgs as a function
of the Higgs mass, and we obtain exclusion regions in the tanB vs mass for
the neutral MSSM Higgs, and branching fraction vs mass for the charged
Higgs.