For some full measure subset B of the set of interval exchange transformations (IETs) the following is satisfied. Let X be a C^r, 1 ≤ r ≤ ∞, vector field, with finitely many singularities, on a compact orientable surface M. Given a non-trivial recurrent point p∈M of X, the holonomy map around p is semi-conjugate to an IET E : [0,1)[0,1). If E∈B then there exists a C^r vector field Y, arbitrarily close to X, in the C^r-topology, such that Y has a closed trajectory passing through p.