Low-order process modeling provides a basis for control system design and on-line autotuning in process control. A systematic on-line identification method is proposed in this article to obtain a second-order-plus-dead-time (SOPDT) model from a single biased/unbiased relay feedback test. The relay response shapes of the three types of SOPDT model, overdamped, critically damped, and underdamped, are first examined and categorized for model structure selection before proceeding with the corresponding parameter identification. Exact expressions of the corresponding limit cycles are derived for assessing process response under relay feedback test. By using the measurable parameters of these limit cycles, the corresponding identification algorithms are subsequently derived in a transparent manner. Two denoising methods are given to cope with measurement noises. Illustrative examples are performed to demonstrate the effectiveness and merits of the proposed identification algorithms. (C) 2008 American Institute of Chemical Engineers.