  The magnetic orders in Na$_2$IrO$_3$ and $\alpha-$RuCl$_3$, honeycomb systems
with strong spin-orbit coupling and correlations, have been recently described
by models with the dominant Kitaev interactions. In this work we discuss how
the orientation of magnetic order parameter is selected in this class of
models. We show that while the order-by-disorder mechanism in the models with
solely Kitaev anisotropies always select cubic axes as easy axes for magnetic
ordering, the additional effect of other small bond-dependent anisotropies,
such as, e.g., $\Gamma$-terms, lead to a deviation of the order parameter from
the cubic directions. We show that both the zigzag ground state and the
face-diagonal orientation of magnetic moments in Na$_2$IrO$_3$ can be obtained
within the $J_1-K_1-J_2-K_2-J_3$ model in the presence of perturbatively small
$\Gamma$-terms. We also show that the zigzag phase found in the nearest
neighbor Kitaev-Heisenberg model, relevant for $\alpha-$RuCl$_3$, has some
stability against the $\Gamma$-term.
