A first-order-plus-dead-time (FOPDT) model is most commonly used for control system design and on-line tuning. By using a single biased/unbiased relay feedback test, four alternative identification algorithms are proposed for obtaining a FOPDT model for a stable process and four alternative FOPDT algorithms for unstable processes. By deriving the exact relay response expressions for FOPDT stable/unstable processes, two of the above algorithms are proposed for implementation simplicity based on some measurable parameters of the relay response, while the other two algorithms are developed with more computation effort for obtaining enhanced accuracy for identification of high-order processes, according to whether a single biased or unbiased relay feedback test is used. A denoising method based on a low-pass Butterworth filter is presented to guarantee identification robustness in the presence of measurement noises. Illustrative examples are given to demonstrate the effectiveness and merits of the proposed identification algorithms.