The nonlinearity of many chemical processes can be approximated by a static nonlinear element in series with a linear dynamic element. The model is called a Hammerstein model if the nonlinear static element precedes the linear dynamic element. It is a Wiener model if the order is reversed. This paper presents a simple method for the experimental determination of both the linear dynamic part and the nonlinear static part of the nonlinear model, simultaneously, by the use of nonlinear auto-tuning (relay feedback). A conventional linear auto-tune test, developed by Astrom and co-workers, is conducted by placing a relay in the feedback loop. The amplitude of the resulting oscillating output and the period of this cycle gives approximate values for the ultimate frequency and the ultimate gain of the linear system. The nonlinear auto-tune method described in this paper consists of the consecutive use of two or more relay-feedback tests with different relay heights and with different known dynamic elements inserted in the loop. For a Hammerstein model, the relays are displaced vertically from the origin such that the oscillations of the output of the process are symmetrical about the steady-state value. For a Wiener model, the relays are shifted horizontally from the origin such that the input to the process is a sequence of symmetrical pulses. The effectiveness of the method is demonstrated on two simulated example nonlinear processes: a simple second-order system with exponential static nonlinearity and a realistically complex distillation column.