  We study spacetime singularities in a general five-dimensional braneworld
with curved branes satisfying four-dimensional maximal symmetry. The bulk is
supported by an analog of perfect fluid with the time replaced by the extra
coordinate. We show that contrary to the existence of finite distance
singularities from the brane location in any solution with flat (Minkowski)
branes, in the case of curved branes there are singularity-free solutions for a
range of equations of state compatible with the null energy condition.
