  In this paper, we study for the first time topological defects in the context
of nonlocal field theories in which Lagrangians contain infinite-order
differential operators. In particular, we analyze domain walls. Despite the
complexity of non-linear infinite-order differential equations, we are able to
find an approximate analytic solution. We first determine the asymptotic
behavior of the nonlocal domain wall close to the vacua. Then, we find a
linearized nonlocal solution by perturbing around the well-known local 'kink',
and show that it is consistent with the asymptotic behavior. We develop a
formalism to study the solution around the origin, and use it to verify the
validity of the linearized solution. We find that nonlocality makes the width
of the domain wall thinner, and the energy per unit area smaller as compared to
the local case. For the specific domain wall solution under investigation, we
derive a theoretical constraint on the energy scale of nonlocality which must
be larger than the corresponding symmetry-breaking scale. We also briefly
comment on other topological defects like string and monopole.
