Résumé : On a (pseudo-)Riemannian manifold (M,g), some fields of endomorphisms i.e. sections of End(TM) may be parallel for g. They form an associative algebra e, which is also the commutant of the holonomy group of g. We study it. As any associative algebra, e is the sum of its radical and of a semi-simple algebra $\goth s$. We show the following: s may be of eight different types, including the generic type s=R.Id, and the Kähler and hyperkähler types s≈C and s≈H. For N any self adjoint nilpotent element of the commutant of s in End(TM), the algebra s x is the algebra of the parallel endomorphisms of a non empty set of germs of metrics, that we parametrise. Generically, the holonomy group of these metrics is the commutant of N in the commutant H(s) of s in SO°(g). To prove it, we introduce an analogy with complex Differential Calculus, the ring R[X]/(X^n) replacing the field C. This describes totally the local situation when the radical of e is principal and consists of self adjoint elements. We add a glimpse on the case where this radical is not principal, and give the constraints imposed to the Ricci curvature when e is non trivial.