SUMMARY The Parkfield segment of the San Andreas fault shows seismic quiescence for M > 2.0 earthquakes since early to mid-1986. The rate decreases by 45 to 70 per cent depending on the magnitude band. We interpret this change as real because it is concentrated in the larger magnitudes and cannot be explained by a reasonable magnitude shift. The rate decrease is present in the Parkfield segment of the fault between 35.6 and 36.1°N, and no other rate change as significant has been observed during the time when high quality data were available (since 1975). We interpret this observation as a seismic quiescence precursor to the next Parkfield mainshock. Although information on the expected duration of precursory quiescence is weak, we estimate that the Parkfield earthquake should occur in the interval 1990 February to 1992 February. Precursory seismic quiescence, which lasted approximately 1.5 yr, was found in, and possibly around, the source volume of an earthquake withM= 3.6 which occurred on 1986 August 29 in the Parkfield area. This observation demonstrates that the quiescence hypothesis is applicable to the Parkfield segment of the San Andreas fault. The false alarm rate was estimated in a detailed analysis as a function of alarm level for the fault segments surrounding the M= 5.0 Stone Canyon (1982 August) and M= 3.6 Parkfield (1986 August) mainshocks. For these two events, the duration and statistical significance of false alarms as a function of space, time and magnitude band was determined. We propose that in this tectonic environment, and with the data characteristics of these earthquake catalogues, attempts to predict mainshocks based on the quiescence hypothesis may be successful and generate one to two false alarms covering about 10 per cent of the time-space dimensions of the catalogue.