  We perform a detailed analysis of the asymptotic behavior of a multifield
cosmological model with phantom terms. Specifically, we consider the
Chiral-Phantom model consisting of two scalar fields with a mixed kinetic term,
while one scalar field has negative kinetic energy, that is, it has phantom
properties. We show that the Hubble function can change sign, and we study the
global evolution of the field equation in the finite and infinity regions with
the use of Poincar\'{e} variables. We find that in the Chiral-Phantom model the
limit of the quintessence scalar field is recovered while the cosmological
evolution differs from the standard hyperbolic theory. Finally, the linear
cosmological perturbations are studied.
