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We present a general phenomenological analysis of a class of Two Higgs Doublet Models with Flavor Changing Neutral Cur-rents arising at the tree level. The existing constraints mainly affect the couplings of the first two generations of quarks, leav-ing the possibility for non negligible Flavor Changing couplings of the top quark open. The next generation of lepton and hadron colliders will offer the right environment to study the physics of the top quark and to unravel the presence of new physics beyond the Standar Model. In this context we discuss some interestin