Abstract: Dark energy rapidly evolving from the dustlike state in the close past to the
phantomlike state at present has been recently proposed as the best fit for the
supernovae Ia data. Assuming that a dark energy component with an arbitrary
scalar-field Lagrangian, which has a general dependence on the field itself and
its first derivatives, dominates in the flat Friedmann universe, we analyze the
possibility of a dynamical transition from the states with w>-1 to those with
w<-1 or vice versa. We have found that generally such transitions are
physically implausible because they are either realized by a discrete set of
trajectories in the phase space or are unstable with respect to the
cosmological perturbations. This conclusion is confirmed by a comparison of the
analytic results with numerical solutions obtained for simple models. Without
the assumption of the dark energy domination, this result still holds for a
certain class of dark energy Lagrangians, in particular, for Lagrangians
quadratic in field's first derivatives. The result is insensitive to topology
of the Friedmann universe as well.