This work is devoted to investigating the coexistence of anti-synchronization (AS) and complete synchronization (CS) of two identical delay hyperchaotic Lü systems via partial variables. Based on the Lyapunov stability theory, a simple synchronization scheme only with linear inputs is considered. The sufficient conditions of synchronization are also obtained for both linear feedback and adaptive control approaches. The coexistence of AS and CS between two nearly identical delay chaotic systems with unknown parameters is explored. A single input controller is proposed and the adaptive parameter update laws are developed. Numerical simulation results are presented to demonstrate the effectiveness of the proposed chaos synchronization scheme.