<p>The growing demand for electrical energy and the focus on renewable energy sources have increased interest in high-voltage direct current (HVDC) transmission systems, especially multi-terminal HVDC (MTDC) systems. MTDC systems offer several advantages, such as connecting multiple AC networks simultaneously, transmitting high power, and providing economic benefits. However, controlling DC line currents remains a significant challenge. The use of DC current flow controllers (CFC) helps regulate and control DC power in these systems. As MTDC systems become more complex, stability analysis and accurate evaluations are essential. A critical challenge in this field is assessing system stability under the influence of interactions between various components. Linear analysis is useful for identifying changes near the operating point, but it is not enough to detect interaction phenomena when power system is subjected to significant nonlinear effects. Thus, nonlinear analysis is necessary to study such phenomena comprehensively. This paper explores the stability of the CFC-MTDC system, considering interactions between system components and the controllers. The mathematical model of the system is derived and using linear modal analysis, examining how parameter and control value changes system damping. Due to the system's nonlinear nature, normal form analysis and associated indices are used to evaluate stability and detect interactions. The system is analyzed in both time and frequency domains by comparing the responses of linear, nonlinear step-by-step, and normal form analysis methods.</p>