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An electron cloud causes various effects in high intensity positron storage rings. The positron beam and the electron cloud can be considered a typical two-stream system with a certain plasma frequency. Beam-beam interaction is another important effect for high luminosity circular colliders. Colliding two beams can be considered as a two-stream system with another plasma frequency. We study the combined phenomena of the beam-electron cloud and beam-beam interactions from a viewpoint of two complex two-stream effects with two plasma frequencies.