  For some full measure subset B of the set of iet's (i.e. interval exchange
transformations) the following is satisfied: Let X be a $C^r$, $1\le r\le
\infty$, vector field, with finitely many singularities, on a compact
orientable surface M. Given a nontrivial recurrent point $p\in M$ of X, the
holonomy map around p is semi-conjugate to an iet $E :[0,1) \to [0,1).$ If
$E\in B$ 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.
