  The electroweak corrections of order ${\cal O}(\alpha_{\rm em}
m^2_{t,b}/m^2_w)$ and ${\cal O}(\alpha_{\rm em} m^3_{t,b}/m^3_w)$ to Higgs
boson associated production with top quark pair are calculated at $e^+e^-$
colliders in the standard model (SM), the two-Higgs-doublet model (2HDM) and
the minimal supersymmetric standard model (MSSM). These corrections are a few
percent in general, and in the MSSM they can be over ten percent for favorable
parameter values allowing by current precise experiments. The total cross
sections including the electroweak corrections get their maximal near $\sqrt{s}
= 700$GeV, and can reach 2.8 fb, 2.7 fb and 2.5 fb in the SM, the 2HDM and the
MSSM, respectively.
