Unknown process parameters are identified using limit cycle data of the relay-response curves obtained from single relay feedback test on second order plus dead time (SOPDT) processes. Time domain analytical expressions of these curves are helpful in deriving conditions to estimate process parameters accurately. Identification algorithms are formulated to estimate minimal number of model parameters of SOPDT processes. The estimation procedure consists of the following steps. A relay feedback test is conducted to obtain a symmetric relay response (if the response is not symmetric we do a biased relay test) and then estimation algorithms are applied. The method is validated for systems with modeling errors or under load and also for systems with and without measurement noise. (c) 2006 Elsevier Ltd. All rights reserved.