  This paper deals with front propagation dynamics of monostable equations with
nonlocal dispersal in spatially periodic habitats. In the authors' earlier
works, it is shown that a general spatially periodic monostable equation with
nonlocal dispersal has a unique spatially periodic positive stationary solution
and has a spreading speed in every direction. In this paper, we show that a
spatially periodic nonlocal monostable equation with certain spatial
homogeneity or small nonlocal dispersal distance has a unique stable periodic
traveling wave solutions connecting its unique spatially periodic positive
stationary solution and the trivial solution in every direction for all speeds
greater than the spreading speed in that direction.
