  The goal of this paper is to construct a category of motivic "sheaves" on an
algebraic variety defined over a subfield of C, using Nori's method. This
categoryis abelian and it possesses faithful exact realization functors to the
categoriesof constructible sheaves for the classical and etale topologies.
Moreover, there is a tannakian subcategory of motivic local systems with a
realization functor into the category of variations of mixed Hodge structures.
Conversely, all basic geometric examples of the latter come from this motivic
category.
