This paper proposes a practical method to identify the process dynamics for an integral process with dead-time, under continuous self-excited oscillation. It is assumed that the limit cycle is mainly caused by either the nonlinear property, dead-time of the process, or inappropriate PI parameters. Oscillatory PI control loops under inappropriate PI parameter settings are often found in actual plants, particularly in slow-response integral processes. The proposed method identifies not only the integral time constant but also the dead time of processes from their period of oscillation and PI parameters. A simple method to design robust PI parameters on the basis of internal model control (IMC) is also shown, where the IMC filter parameter is derived from the phase/gain margin and dead-time of the process. The process identification method and robust PI design method are successfully applied to an actual approximate integral process with self-excited oscillation. The proposed method does not require a step response test, which are best avoided in actual plant environments.