  We show that in multidimensional gravity vector fields completely determine
the structure and properties of singularity. It turns out that in the presence
of a vector field the oscillatory regime exists for any number of spatial
dimensions and for all homogeneous models. We derive the Poincar\'e return map
associated to the Kasner indexes and fix the rules according to which the
Kasner vectors rotate. In correspondence to a 4-dimensional space time, the
oscillatory regime here constructed overlap the usual
Belinski-Khalatnikov-Liftshitz one.
