  The first effective versions of Faltings product theorem are given by J.H.
Evertse and R. Ferretti. Their results are improved quantitatively by P.
Philippon, thanks to Samuel's multiplicity instead of the length in his zeros
estimate. This version is a generalization of the usuel Roth's lemma on powers
of the additive group. Here following this approach with some modifications, we
obtain an analogue of the theorem for any product of commutative algebraic
groups.
