  We investigate the phase-space structure of the quintom dark energy paradigm
in the framework of spatially flat and homogeneous universe. Considering
arbitrary decoupled potentials, we find certain general conditions under which
the phantom dominated solution is late time attractor, generalizing previous
results found for the case of exponential potential. Center Manifold Theory is
employed to obtain sufficient conditions for the instability of de Sitter
solution either with phantom or quintessence potential dominance.
