It is well‐known that, when the bunch current in an electron storage ring exceeds a certain value, the bunch length becomes longer than the natural length determined by the balance between the radiation damping and excitation. The threshold current can be estimated by the linearized Vlasov equation, but the problem of the bunch length above threshold cannot be treated by the linear theory. In the present report, we discuss a method which gives a steadily oscillating state above threshold in the framework of the quasilinear method in the plasma physics. ©1996 American Institute of Physics.