In nonlinear blind source separation (BSS) independence is not sufficient to recover the original source signal and additional criteria are needed to sufficiently constrain the optimization problem. Here we introduce autoregressive (AR) parameters as criteria and combined with expansion space develop a new method, which lead to a unique solution of the nonlinear BSS problem. The proposed method is based on two key assumptions. One lies in that a source signal’s AR parameters can be roughly estimated before operation, and the other is that expansion space, such as kernel feature space, should be chosen rich enough to approximate the nonlinearity. This method can extract the desired source signal as a unique solution with the help of this signal’s AR parameter, or it extracts one signal at one time. Thus it is also referred to as nonlinear blind source extraction (BSE). Its performance is demonstrated on nonlinearly mixed speech data.