Purpose <p>This study investigates the complex dynamics and codimension-two bifurcations in a delayed mutually coupled optoelectronic system. The objective is to analyze the effects of feedback delay and coupling strength on the system dynamics and to provide insights that enhance the reliability and performance of optoelectronic and photonic technologies used in optical communication and signal processing.</p> Methodology <p>DDE-BIFTOOL is employed to construct bifurcation diagrams with respect to the feedback delay parameter (τ) and coupling strength parameter (β), enabling the identification of double-Hopf bifurcation points. The method of multiple scales (MMS) is then applied to derive complex amplitude equations near the bifurcation points. Furthermore, the method of normal form is used to classify and unfold the bifurcation behavior and determine the stability characteristics of the resulting solutions.</p> Findings <p>The analysis reveals the existence of several double-Hopf bifurcation points and demonstrates a variety of complex dynamical behaviors. Stable equilibrium states, stable periodic oscillations, and bistability of periodic solutions are identified in specific parameter regions. Additionally, more intricate dynamics, including stable almost-periodic solutions and phase-locked solutions, are observed. The system is shown to transition to chaos through different routes depending on the varying parameter: chaos emerges through a period-5 window when β varies, whereas a period-doubling bifurcation route to chaos is observed when τ varies.</p> Originality/Value <p>This work provides a comprehensive bifurcation analysis of a delayed, mutually coupled optoelectronic system, with an emphasis on codimension-two dynamics and the unfolding of a double-Hopf bifurcation. The results contribute to a deeper understanding of nonlinear behaviors in optoelectronic systems and offer valuable theoretical guidance for the design and optimization of advanced photonic devices and communication systems.</p>