We consider the double exchange for systems in which doped electrons occupy degenerate orbitals, treating the realistic situation with double degenerate e_g orbitals. We show that the orbital degeneracy leads in general to the formation of anisotropic magnetic structures and that, in particular, depending on the doping concentration, the layered magnetic structures of the A-type and the chainlike structures of the C-type are stabilized. The phase diagram that we obtain provides an explanation for the experimentally observed magnetic structures of some overdoped (electron-doped) manganites of the type Nd_{1 − x}Sr_xMnO₃Pr_{1 − x}Sr_xMnO₃and Sm_{1 − x}Ca_xMnO₃with x > 0.5.