The appearance of the chaotic synchronization regimes has been discovered for the coupled spatially extended beam–plasma Pierce systems. The coupling was introduced only on the right bound of each subsystem. It has been shown that with coupling increase the spatially extended beam–plasma systems show the transition from asynchronous behavior to the phase synchronization and then to the complete synchronization regime. For the consideration of the chaotic synchronization we used the concept of time-scale synchronization described in work [A.E. Hramov, A.A. Koronovskii, Chaos 14 (3) (2004) 603] and based on the introduction of the continuous set of phases of chaotic signal. In case of unidirectional coupling the generalized synchronization regime has been observed in the spatially extended beam–plasma systems. The generalized synchronization appearance mechanism has been analyzed by means of the offered modified system approach [A.E. Hramov, A.A. Koronovskii, Phys. Rev. E 71 (6) (2005) 067201].