In this paper, we introduce certain type of pro-object in the
triangulated category geometric mixed motives defined by
V. Voevodsky. These pro-motives are attached to a finite type extension
of the base field and to an integer and are called generic motives
(with weight).
Especially, we show that these generic motives are subject to a
functoriality which is dictated by the axioms of a cycle pre-module as
defined by M. Rost. This involves in particular a study of the
functoriality of triangulated mixed motives such as the functoriality
of the Gysin triangle.
These results show in particular that any cohomology which induces a
realisation functor from the category of triangulated mixed motives
defines canonically a cycle module.
[ preprint updated Jan 13, 2006, replacing one dated May 7, 2004. ]