  We study the competition between different possible ground states of the
double-exchange model with strong ferromagnetic exchange interaction between
itinerant electrons and local spins. Both for classical and quantum treatment
of the local spins the homogeneous canted state is shown to be unstable against
a phase separation. The conditions for the phase separation into the mixture of
the antiferromagnetic and ferromagnetic/canted states are given. We also
discuss another possible realization of the phase-separated state:
ferromagnetic polarons embedded into an antiferromagnetic surrounding. The
general picture of a percolated state, which emerges from these considerations,
is discussed and compared with results of recent experiments on doped
manganaties.
