The Hubbard model with extended hoppings on a cubic lattice is shown to hav
e antiferromagnetic phases displaying long-range order, when the temperatur
e is small and the repulsive Coulomb potential is sufficiently strong. Our
results are rigorous in the case of the asymmetric Hubbard model. Besides c
hessboard states, stabilizing effects of hopping yield other phases, such a
s planar and lamellar ones, depending on the relative strength of the hoppi
ng coefficients.