  We report on results obtained at the Tevatron by the CDF and D0
collaborations up to June 2008 (2.4 fb-1), on searches for standard model (SM)
Higgs bosons having a high mass (135-200 GeV). High mass Higgs bosons decay
dominantly in WW and the presented searches are performed in the leptonic decay
modes of the W's. Both direct production (ppbar -> H) and associated production
(ppbar -> WH) are studied and eventually combined with all channels available
at the Tevatron. Prospects for SM Higgs searches with the full projected
Tevatron statistics are also given.
