We investigate a system consisting of multiple ring lasers coupled by a single gain medium. All the ring lasers share a common feedback arm. The output power of an individual laser shows periodic oscillations as a function of time. The periodicity of the oscillation is determined by the ratio of the roundtrip times of the feedback arm and the ring cavity. In the case that two of such ring lasers are coupled, either their oscillation periodicities are synchronized, or the system is bi-stable. In the latter operation regime, the system can act as an optical flip-flop memory whose state be switched by injection of external light. The concept can be extended to multi-state operations; an eight-state optical flip-flop memory is experimentally demonstrated. ?? 2006 Elsevier B.V. All rights reserved.