  This paper establishes the long time asymptotic limit of the three
dimensional Vlasov-Poisson equation with strong external magnetic field. The
guiding center approximation is investigated in the three dimensional case with
a non-constant magnetic field. In the long time asymptotic limit, the motion
can be split in two parts : one stationary flow along the lines of the magnetic
field and the guiding center motion in the orthogonal plane of the magnetic
field where classical drift velocities are recovered. We discuss in particular
the effect of nonconstant external magnetic fields.
