  We study the anisotropic magnetic structures exhibited by electron-doped
manganites using a model which incorporates the double-exchange between orbital
ly degenerate $e_{g}$ electrons and the super-exchange between $t_{2g}$
electrons with realistic values of the Hund's coupling($J_H$), the
super-exchange coupling($J_{AF}$), and the bandwidth($W$). We look at the
relative stabilities of the G, C and A type antiferromagnetic ph ases. In
particular we find that the G-phase is stable for low electron doping as seen
in experiments. We find good agreement with the experimentally observed
magnetic phase diagrams of electron-doped manganites
  ($x > 0.5$) such as Nd$_{1-x}$Sr$_{x}$MnO$_{3}$, Pr$_{1-x}$Sr$_{x}$MnO$_{3}$,
and Sm$_{1-x}$Ca$_{x}$MnO$_{3}$. We can also explain the experimentally
observed orbital structures of the C a nd A phases.
  We also extend our calculation for electron-doped bilayer manganites of the
form R$_{2-2x}$A$_{1+2x}$Mn$_2$O$_7$ and predict that the C-phase will be
absent in t hese systems due to their reduced dimensionality.
