  In this paper we prove the breakdown of the two-dimensional stable and
unstable manifolds associated to two saddle-focus points which appear in the
unfoldings of the Hopf-zero singulariry. The method consists in obtaining an
asymptotic formula for the difference between this manifolds which turns to be
exponentially small respect to the unfolding parameter. The formula obtained is
explicit but depends on the so-called Stokes constants, which arise in the
study of original vector field and which corresponds to the so called inner
equation in singular perturbation theory.
