  A certain class of nonlocal theories eliminates an arbitrary cosmological
constant (CC) from a universe that can be perceived as our world. Dark energy
then cannot be explained by a CC; it could however be due to massive gravity.
We calculate the new corrections, which originate from the nonlocal terms that
eliminate the CC, to the decoupling limit Lagrangian of massive gravity. The
new nonlocal terms also have internal field space Galilean symmetry and are
referred here as "nonlocal Galileons." We then study a self-accelerated
solution and show that the new nonlocal terms change the perturbative stability
analysis. In particular, small fluctuations are now stable and non-superluminal
for some simple parameter choices, whereas for the same choices the pure
massive gravity fluctuations are unstable. We also study stable spherically
symmetric solutions on this background.
