  This paper is devoted to the study of some coherent sheaves on non reduced
curves that can be locally embedded in smooth surfaces. If Y is such a curve
then there is a filtration by subschemes C_i such that C_1 is the reduced curve
associated to Y, and that for every P in C, if z is an equation of C_1 in the
local ring of Y at P, then (z^i) is the ideal of C_i. A coherent sheaf on Y is
called torsion free if it does not have any non zero subsheaf with finite
support. We prove that torsion free sheaves are reflexive. We study then the
quasi locally free sheaves, i.e. sheaves which are locally isomorphic to direct
sums of the structure sheaves of the C_i. We define an invariant for these
sheaves, the complete type, and prove the irreducibility of the set of sheaves
of given complete type. We study the generic quasi locally free sheaves, with
applications to the moduli spaces of stable sheaves on Y.
