  We analyse the intersection of positively and negatively sectional-hyperbolic
sets for flows on compact manifolds. First we prove that such an intersection
is hyperbolic if the intersecting sets are both transitive (this is false
without such a hypothesis). Next we prove that, in general, such an
intersection consists of a nonsingular hyperbolic set, finitely many
singularities and regular orbits joining them. Afterward we exhibit a
three-dimensional star flow with two homoclinic classes, one being positively
(but not negatively) sectional-hyperbolic and the other negatively (but not
positively) sectional-hyperbolic, whose intersection reduces to a single
periodic orbit. This provides a counterexample to a conjecture by Shy, Zhu, Gan
and Wen (\cite{sgw}, \cite{zgw}).
