The two-axis coupled electromechanical actuation system (TCEAS) is widely utilized in multiple industrial fields, but its tracking performance and stability are severely hampered by complex nonlinear friction, parameter uncertainties, and strong coupling effects. To address these issues, this paper proposes an adaptive robust stable tracking control (ARSTC) method with friction compensation. First, the friction characteristic of TCEAS is analyzed and a continuously differentiable friction moment function is introduced to accurately describe the nonlinear friction phenomenon. Then, a dynamic analysis model for the system considering friction nonlinearity and model uncertainty is established. Furthermore, the developed ARSTC algorithm leverages adaptive control to estimate and compensate unknown friction parameters (enhancing precision) and robust control to suppress disturbances (ensuring stability). Finally, the superiority is jointly verified by stability analysis and extensive comparative numerical test results. This work demonstrates a practical approach for high-precision control of TCEAS, which has important theoretical significance.