A token passing ring can be described as a system of ni queues with one server that rotates around the queues sequentially, Georgiadis and Szpankowski [4, pp. 7-33] considered rings where the token (server) performs x Lambda l(j) services on queue j, where x is the size of queue j upon arrival of the token, and l(j) is a fixed limit of service for queue j. The token then spends same random time switching to the next queue. For j = 1, ... , M, arrivals to queue j are Poisson with rate lambda(j), and service times have means s(j) and are independent of the arrival and switchover processes. The purpose of this paper is to give an alternate and simpler proof of the stability conditions given in [4] using Lyapunov functions. An additional assumption is made about the second moments of the service and switchover times being finite.