  The possibility of observing large signatures of new CP-violating and
flavor-changing Higgs-Top couplings in a future e^+e^- collider experiments
such as e^+e^- -> t bar-t h, t bar-t Z and e^+e^- -> t bar-c \nu_e bar-\nu_e, t
bar-c e^+ e^- is discussed. Such, beyond the Standard Model, couplings can
occur already at the tree-level within a class of Two Higgs Doublets Models.
Therefore, an extremely interesting feature of those reactions is that the
CP-violating and flavor-changing effects are governed by tree-level dynamics.
These reactions may therefore serve as unique avenues for searching for new
phenomena associated with Two Higgs Doublets Models and, as is shown here,
could yield statistically significant signals of new physics. We find that the
CP-asymmetries in e^+e^- -> t bar-t h, t bar-t Z can reach tens of percents,
and the flavor changing cross-section of e^+e^- -> t bar-c \nu_e bar-\nu_e is
typically a few fb's, for light Higgs mass around the electroweak scale.
