  Let S be a scheme. In this paper, we define the notion of biextensions of
1-motives by 1-motives. If M(S) denotes the Tannakian category generated by
1-motives over S (in a geometrical sense), we define geometrically the
morphisms of M(S) from the tensor product of two 1-motives M_1 and M_2 to
another 1-motive M_3, to be the isomorphism classes of biextensions of
(M_1,M_2) by M_3. Generalizing this definition we obtain, modulo isogeny, the
geometrical notion of morphism of M(S) from a finite tensor product of
1-motives to another 1-motive.
