Abstract: In describing various modes of chaotic oscillators, generalized winding numbers are defined in tangent space corresponding to Lyapunov exponents of the chaotic attractor. Bifurcation behaviors from synchronous chaos of coupled Duffing oscillators are investigated using these concepts. The results show that a kind of Hopf bifurcation can take place from the synchronous chaotic state. Analysis of power spectrum indicates that the characteristic frequency created by the Hopf bifurcation is equal to the generalized winding number of the critical transverse modes just before the bifurcation.