  A mutualist model with nonlocal diffusions and a free boundary is first
considered. We prove that this problem has a unique solution defined $t\ge0$,
and its dynamics are governed by a spreading-vanishing dichotomy. Some criteria
for spreading and vanishing are also given. Of particular importance is that we
find that the solution of this problem has quite rich longtime behaviors, which
vary with the conditions satisfied by kernel functions and are much different
from those of the counterpart with local diffusion and free boundary. At last,
we extend these results to the model with nonlocal diffusions and double free
boundarie
