Sur les conditions d'existence des faisceaux semi-stables sur les courbes multiples primitives

We give sufficient conditions for the (semi-)stability of torsion free sheaves on a primitive multiple curve. These conditions are used to prove that some moduli spaces of stable sheaves are not empty. We study mainly the quasi locally free sheaves of generic type (this includes the locally free sheaves). These sheaves are generic, i.e. for every moduli space of torsion free sheaves, the sheaves of this type correspond to an open subset of the moduli space.