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In this paper, we consider the large time asymptotic behavior of solutions tosystems of two cubic nonlinear Schr"odinger equations in one space dimension.It turns out that for a system there exists a small solution of whichasymptotic profile is a sum of two parts oscillating in a different way. Thiskind of behavior seems new. Further, several examples of systems which admitsolution with several types of behavior such as modified scattering, nonlinearamplification, and nonlinear dissipation, are given. We also extend ourprevious classification result of nonlinear cubic systems.

Asymptotic behavior in time of solution to system of cubic nonlinear Schr"odinger equations in one space dimension