  The direct CP-asymmetry in the inclusive $B \to X_d \gamma$ and $B \to X_d
e^+ e^ - $ decays is investigated in the two-Higgs doublet extension of the
Standard Model (2HDM). The investigation is performed in the lowest
non-vanishing order of the perturbation theory using the existing restrictions
on the 2HDM parameters space. It is shown that the direct CP-asymmetry in the
$B \to X_d \gamma$ decay can deviate significantly from the Standard Model
predictions. In the presence of only one source of CP-violation (the CKM matrix
weak phase) $a_{CP}(B \to X_d \gamma)$ can have the sign opposite to that in
the SM. The new source of CP-violation can make $|a_{CP}(B \to X_d \gamma)|$
arbitrary small (unlike the SM case) and hence unmeasurable. Quantitatively,
the obtained results suffer from the uncertainty of the choice of
renormalization scale. As for the $B \to X_d e^+ e^ - $ rate asymmetry, its
renormalization scale dependence in the lowest non-vanishing order does not
allow to conclude if this quantity is efficient for testing New Physics beyond
the Standard Model.
