We consider the phenomenology of a fermiophobic Higgs boson (h_f) at the
Large Hadron Collider (LHC) and a e+e- Linear Collider (LC). At both machines
the standard production mechanisms which rely on the coupling h_fVV (V=W,Z) can
be very suppressed at large tan beta. In such cases the complementary channels
pp to H^\pm h_f, A^0 h_f and e+e- to A^0 h_f offer promising cross-sections.
Together with the potentially large branching ratios for H^\pm to h_fW* and A^0
to h_fZ*, these mechanisms would give rise to double h_f production, leading to
signatures of gamma gamma gamma gamma, gamma gamma VV and VVVV.Comment: 19 pages, 9 figures, expanded discussion, fig.1 changed slightly,
version to appear in Phys.Rev.