A reasonable description of the system dynamics is one of the key elements to achieve high performance control for accelerating modules. This paper depicts the system identification of a cross-coupled pair of cavities for the Relativistic Electron Gun for Atomic Exploration - REGAE. Two normal conducting copper cavities driven by a single RF source accelerate and compress a low charge electron bunch with sub 10 fs length at a repetition rate up to 50 Hz. It is shown how the model parameters of the cavities and the attached radio frequency subsystem are identified from data generated at the REGAE facility