  In this paper, we generalize the direct method of moving planes for the
fractional Laplacian to the system case. Considering a coupled nonlinear system
with fractional Laplacian, we first establish a decay at infinity principle and
a narrow region principle. Using these principles, we obtain two radial
symmetry results for the decaying solutions of the fractional Laplacian
systems. Our method can be applied to fractional Schr\"odinger systems and
fractional H\'enon systems.
