Deformation de fibres vectoriels sur les varietes lisses de dimension trois

Let X be a smooth 3-fold and let E be a rank 2 torsion free sheaf. In the first part of this paper, we give some necessary conditions for the sheaf E to be limit of vector bundles. In the second part, we describe an example of this problem. Thanks to the construction of Ellingsrud and Stromme, we describe a familly of rank 2 sheaves on P^3 (the 3-dimensional projective space). We show that for this familly, the conditions of the first part are sufficient.