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In this paper, we consider the scattering problem for a class of $N$-coupledsystems of the cubic nonlinear Schr\"odinger equations in three spacedimensions. We prove the scattering of solutions that have a mass-energyquantity less than that for the ground states. This result is previouslyobtained by Duyckaerts-Holmer-Roudenko for the single cubic nonlinearSchr\"odinger equation in three space dimensions. It turns out that the resultcan be extended to a wide class of $N$-coupled systems.

Scattering below ground states for a class of systems of nonlinear Schrodinger equations