In positron or proton storage rings with many closely spaced bunches,an ele
ctron cloud can build up in the vacuum chamber due to photoemission or seco
ndary emission. We discuss the possibility of a single-bunch two-stream ins
tability driven by this electron cloud. Depending on the strength of the be
am-electron interaction, the chromaticity and the synchrotron oscillation f
requency, this instability either resembles a linac beam breakup or a head-
tail instability. We present computer simulations of the instabilities, and
compare the simulation results with analytical estimates.