  We show that the statement analogous to the Mumford-Tate conjecture for
abelian varieties holds for 1-motives on unipotent parts. This is done by
comparing the unipotent part of the associated Hodge group and the unipotent
part of the image of the absolute Galois group with the unipotent part of the
motivic fundamental group. Contains an appendix by P. Deligne.
  In this version: Minor corrections here and there. The Main result about the
image of the Galois representations is now enriched by an adelic statement.
