<p>When it comes to the coordination of multi-agent systems (MASs), the role of containment control cannot be underestimated. Secure containment consensus is the key to facilitating the cooperative work of MASs suffering from malicious attacks. Moreover, the system may encounter situations, such as unavailable state information and time-varying delays, which pose challenges for consensus. This study aims to explore how the directed complex-valued multi-agent systems (DCVMASs) with time-varying delays achieve secure containment consensus under link attacks or denial-of-service attacks. A distributed control protocol based on observer states is proposed, not only guarantees that all followers converge to the convex hull formed by multiple leaders, but also makes the DCVMASs resilient to malicious cyber-attacks. The secure containment consensus control of DCVMASs subject to cyber-attacks is transformed into the stability issue of complex-valued switched error-systems with time-varying delays. Sufficient criteria on containment consensus among agents under different aperiodic attacks are established. Finally, the theoretical results are evidenced by simulation examples.</p>