A homoclinic class of a vector field is the closure of the set of transverse homoclinic points associated to a hyperbolic periodic orbit.We prove the following properties. 1.The homoclinic classes of generic C¹ vector fields on n-manifolds are maximal transitive sets, they are satured sets and isolated if and only if (omega)-isolated . 2. Generic C¹ vector fields do not exhibit cycles associated to homoclinic classes. 3.Codimension 1 singularities, i.e. with a unique positive or negative eigenvalue, of generic C¹ vector fields are contained in maximal transitive sets. 4.Generic C¹ vector fields with finitely many homoclinic classes have finitely many attractors the union of the basins of which form an open dense set of the manifold. 5. There are locally residual sets of C¹ vector fields on a 5-manifold exhibitinf finitely many attractors and repellers but infinitely many homoclinic classes. We also show a sufficient condition for an attracting set to be C¹ weakly robust. Let us observe that these results generalize well Known properties of Axiom a vector fields.