  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.
