We have studied the effect of the third-order density fluctuations in the medium on the collective excitations in quark-gluon plasma. We show that the nonlinear response of a quark-gluon plasma medium leads to non-Abelian collective excitations. We present two kinds of non-Abelian oscillation solutions which respectively correspond to weakly and strongly nonlinear coupling of field components in the color space. We also show that the weakly nonlinear solution is similar to the Abelian-like one but has a frequency shift, which is of order g2T, from the eigenfrequency.