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This paper is devoted to the study of some coherent sheaves on non reducedcurves that can be locally embedded in smooth surfaces. If Y is such a curvethen there is a filtration by subschemes C_i such that C_1 is the reduced curveassociated to Y, and that for every P in C, if z is an equation of C_1 in thelocal ring of Y at P, then (z^i) is the ideal of C_i. A coherent sheaf on Y iscalled torsion free if it does not have any non zero subsheaf with finitesupport. We prove that torsion free sheaves are reflexive. We study then thequasi locally free sheaves, i.e. sheaves which are locally isomorphic to directsums of the structure sheaves of the C_i. We define an invariant for thesesheaves, the complete type, and prove the irreducibility of the set of sheavesof given complete type. We study the generic quasi locally free sheaves, withapplications to the moduli spaces of stable sheaves on Y.

Faisceaux sans torsion et faisceaux quasi localement libres sur les courbes multiples primitives