Transverse e-p instability in proton rings could be damped by increasing the beam density and the rate of secondary particles production above the threshold level, with the corresponding decrease of unstable wavelength Lambda below the transverse beam size h (increase of beam density n(sub b) and ion density n(sub i) above the threshold level: n(sub b) plus n(sub i) greater than Beta (sup 2)/(r(sub e) h(sup 2)), where r(sub e) equals e (sup 2) /mc(sup 2). In this paper, we review experimental observations of transverse instability of proton beams in various rings. We also discuss methods which can be used to damp the instability.