  We study magnetically ordered phases and their phase boundaries in the
$J_1-J_2-J_3$ Heisenberg models on the honeycomb lattice using series
expansions around N\'eel and different colinear and non-colinear magnetic
states. An Ising anisotropy ($\lambda=J_{\perp}/J_z\ne 1$) is introduced and
ground state energy and magnetization order parameter are calculated as a power
seies expansion in $\lambda$. Series extrapolation methods are used to study
properties for the Heisenberg model ($\lambda=1$). We find that at large $J_3$
($>0.6$) there is a first order transition between N\'eel and columnar states,
in agreement with the classical answer. For $J_3=0$, we find that the N\'eel
phase extends beyond the region of classical stability. We also find that
spiral phases are stabilized over large parameter regions, although their
spiral angles can be substantially renormalized with respect to the classical
values. Our study also shows a magnetically disordered region at intermedaite
$J_2/J_1$ and $J_3/J_1$ values.
