We describe a number of multiplexing techniques which may be used for fibre optic sensors in which the sensing element is a ring resonator. The basic optical unit comprises a sensing ring resonator connected to a second interrogating ring resonator of nearly equal length, and illuminated by a source of short coherence length. Using such an arrangement, the high finesse of the ring resonator may be exploited to yield a sensor of increased sensitivity over that obtainable with a two-beam interferometer. A number of such units may be combined to form an array, using coherence multiplexing techniques. When a high coherence source is used, then multiplexing may be accomplished using frequency division techniques. However, in this case, the resonators must have low finesse, in order to avoid cross-talk. We also show that when a source of moderate coherence length is used, it is possible to use both frequency division and coherence multiplexing simultaneously, with the potential of realising a large sensor array.