We study various channels of top and Higgs Flavor Changing Neutral Couplings (FCNC) in the two Higgs doublet Model with natural flavor conservation (2HDM-I and 2HDM-II). We update known results about t → cγ , cZ , cg and comment on t → ch 0 . The decays t → ch 0 as well as {h 0 , H 0 } →tc are sensitive both to the bottom Yukawa coupling as well as to the trilinear scalar couplings h 0 H + H − and H 0 H + H − . After imposing unitarity constraints as well as vacuum stability conditions on scalar sector parameters, in 2HDM-II we found that for large tan β > ∼ 40 and rather light charged Higgs mass M H± < ∼ 150 GeV, the maximum values allowed for Br(t → ch 0 ), Br(H 0 →tc) and Br(h 0 →tc) are: 8 × 10 −5 , 10 −3 and 10 −4 respectively. For charged Higgs mass in the range [200, 300] GeV, which can accommodate B → X s γ constraint if one takes into account large theoretical uncertainties, the branching ratio of both H 0 →tc and h 0 →tc can still be slightly larger than 10 −5 . For A 0 →tc, its branching ratio is smaller than ≈ 10 −7 in both 2HDM-I and 2HDM-II. We study also the top-charm associated production at e + e − colliders and its γγ option as well as at muon colliders. It is found that the cross section of γγ →tc can be of the order 0.01 → 0.1 fb near threshold region, while the cross section of e + e − →tc is well below 10 −2 fb. The situation is slightly better for muon colliders where a few fb cross section can be reached for large tan β and low center of mass energy √ s < ∼ 500GeV.