In the area 30-33°S, 116-118°E of the Southwest Seismic Zone of Western Australia, ML -4.0 earthquakes for the period 1960-1983 do not fit a Poisson model. However, when foreshocks and aftershocks are excluded, the hypothesis of a Poisson distribution cannot be rejected for the resulting series of main shocks. A similar result holds for the subset of ML -5.0 events for the period 1949- 1983. Consequently, when earthquake risk is being assessed by methods that assume a Poisson distribution, foreshocks and aftershocks should be excluded . However, the consequent apparent reduction of risk caused by removing these potentially damaging earthquakes should be pointed out. Although records of seismicity are probably incomplete for the early part of this century, there appears to have been an increase in numbers of ML -4.0 events, starting around 1949. Although, the data are too uncertain to test the increase in the ML -4.0 main shocks statistically, there has been an approximate five-fold increase in the mean yearly number of ML -4.5 main shocks during the period 1949 to 1983, compared with the period 1923 to 1948. This is clearly larger than would be expected from a Poisson process. Consequently, the apparent increase in the number of ML -4.0 events is probably also real and not an artefact of a Poisson process. Also, there were no ML -5.0 events during the period 1923 to 1948, and the only two ML -6.0 earthquakes this century took place in 1968 and 1979. This increase in seismicity since the late 1940s should be taken into account in the interpretation of earthquake risk calculations.