We present sufficient and necessary conditions for stability of token passing rings with time-limited discipline and more generally, a class of monotonic and contractive service disciplines. In general, establishing stability for multidimensional distributed systems is a difficult problem. The standard Lyapunov test function method often fails when applied to such systems (e.g., token passing rings, ALOHA-type sys, rings with spatial reuse, couple-processor system, etc.). In our recent work on this topic we establish a useful alternative approach that turns out to be successful for deriving stability conditions for several distributed systems. In the current paper, we show that our approach can be extended so that it can be applied to the system under consideration.