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