  We introduce the notion of extension of 1-motives. Using the dictionary
between strictly commutative Picard stacks and complexes of abelian sheaves
concentrated in degrees -1 and 0, we check that an extension of 1-motives
induces an extension of the corresponding strictly commutative Picard stacks.
We compute the Hodge, the de Rham and the l-adic realizations of an extention
of 1-motives. Using these results we can prove Deligne's conjecture on
extensions of 1-motives.
