This paper describes two new methods for obtaining frequency response and step response models for processes operating under relay feedback control. Both methods are based on the frequency sampling filter (FSF) model structure and a recursive least-squares (RLS) estimator. With the first method, a standard relay feedback experiment is performed and the FSF/RLS algorithm is used along with the generated input-output data to provide real-time estimates of the process frequency response at the dominant harmonics of the limit cycle. In the second method, a novel relay experiment is proposed that involves switching the error signal back-and-forth between a standard relay element and an integrator in series with a relay. The FSF/RLS algorithm is then applied to the generated process input-output data to obtain a real time estimate of the process step response.