Let S be a scheme. In this paper, we define the notion of biextensions of 1-motives by 1-motives. Moreover, 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 M1⊗M2 to another 1-motive M3, to be the isomorphism classes of biextensions of (M1, M2) by M3: HomM(S)(M1 ⊗...