In this paper, the nonlinear phenomenon known as Hopf bifurcation, chaos, and asynchronous operation of a simple power system are explored. Firstly, taking into account the nonlinearity of the generator shaft and the interaction of mechanics and electrics in the generator sets, we get a transient model by combining Park equations and mechanics equations. Then the Hopf bifurcation, period-doubling bifurcation, and chaos caused by too large a line resistance are investigated with nonlinear mode and Floquet theory. The bifurcation figure of the system is also given. Further study shows that the chaos attractor breaks up into asynchronous operation when the resistance becomes larger. This way of loss-of-stability is different from that caused by loss-of-excitation.