  We give a description of the $\Cone$-interior ($\Int^1(\OrientSh)$) of the
set of smooth vector fields on a smooth closed manifold that have the oriented
shadowing property. A special class $\Bb$ of vector fields that are not
structurally stable is introduced. It is shown that the set
$\Int^1(\OrientSh\setminus\Bb)$ coincides with the set of structurally stable
vector fields. An example of a field of the class $\Bb$ belonging to
$\Int^1(\OrientSh)$ is given. Bibliography: 18 titles.
