  Flavor Changing Neutral Current decays of the top quark within the strict
context of the Standard Model are known to be extremely rare. In fact, they are
hopelessly undetectable at the Tevatron, LHC and LC in any of their scheduled
upgradings. Therefore, if a few of these events eventually show up in the
future we will have certainly discovered new physics. We argue that this could
well be the case for the LHC and the LC both within the Minimal Supersymmetric
Standard Model (MSSM) and in a general two-Higgs-doublet model (2HDM),
especially if we look for FCNC top quark decays into Higgs bosons.
