A search for gamma-gamma decays of a Higgs boson is performed in the data sample collected at LEP with the ALEPH detector between 1991 and 1999. This corresponds to an integrated luminosity of 672 pb-1 at centre-of-mass energies ranging from 88 to 202 GeV. The search is based on topologies arising from a Higgs boson produced in association with a fermion pair via the Higgs-strahlung process e+e- -> Hff, with ff=nu\nu, e+e-, mu+mu-, tau+tau- or qq. Twenty-two events are selected in the data, while 28 events are expected from standard model processes. An upper limit is derived, as a function of the Higgs boson mass, on the product of the e+e- -> Hff cross section and the H -> gamma-gamma branching fraction. In particular, a fermiophobic Higgs boson produced with the standard model cross section is excluded at 95% confidence level for all masses below $100.7 GeV.

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