The most general Two Higgs Doublet Model potential without explicit CP viol
ation depends on 10 real independent parameters. Excluding spontaneous CP v
iolation results in two 7 parameter models. Although both models give rise
to 5 scalar particles and 2 mixing angles, the resulting phenomenology of t
he scalar sectors is different. If flavour changing neutral currents at tre
e level are to be avoided, one has, in both cases, four alternative ways of
introducing the fermion couplings. In one of these models the mixing angle
of the CP even sector can be chosen in such a way that the fermion couplin
gs to the lightest scalar Higgs boson vanishes. At the same time it is poss
ible to suppress the fermion couplings to the charged and pseudo-scalar Hig
gs bosons by appropriately choosing the mixing angle of the CP odd sector.
We investigate the phenomenology of both models in the fermiophobic limit a
nd present the different branching ratios for the decays of the scalar part
icles. We use the present experimental results from the LEP collider to con
strain the models.