Background <p>Nonlinear oscillatory systems with fractal properties and variable stiffness present analytical challenges, particularly in stability analysis and resonance characterization.</p> Objective <p>This study applies the Renormalization Method (RM) to determine system frequency and simplify the analysis of fractal 2DOF nonlinear oscillatory systems by converting non-autonomous forms into equivalent autonomous ones.</p> Methods <p>The RM, which accommodates unrestricted excitation amplitude, was combined with the two-scale methodology and the Harmonic Equivalent Linearization Approach (HELA). Mean square forms were employed to disentangle nonlinear interactions, while the internal resonance technique was incorporated to study coupling effects.</p> Results <p>The proposed framework replicated conventional approaches and enhanced nonlinear interaction analysis. Numerical validations demonstrated that decreasing the fractal dimension value exerts a stabilizing effect on system dynamics.</p> Conclusion <p>The integrated RM–HELA approach provides a robust tool for predicting, simplifying, and controlling dynamic responses in complex nonlinear systems, with strong applicability in physics and engineering.</p>