The existence condition for bistability, B2G > 1, in a one‐coupler single‐mode optical fiber ring resonator using two different all‐fiber schemes of degenerate two‐wave mixing (DTWM) is studied in detail. It is shown that the existence condition for bistability is in general a necessary condition only, not a sufficient condition for the occurrence of the DTWM bistability. © 1994 John Wiley & Sons, Inc.