An investigation is made of the correlograms and smoothed spectral curves of series of monthly and annual precipitation data from stations in different rainfall regimes of the Australian region. The objects of the study are, in the first place, to ascertain whether significant trends or discontinuities are present within any or all of the series. Then, where the data are shown to be stationary, an investigation is made to determine whether significant periodicities exist. The defining of “practical significance" as the level of significance at which a relationship has real value as a predictor in a regression equation results in the rejection of some relationships which are significant only in the statistical sense. Throughout the paper seasonal effects have been eliminated by considering series of annual rainfall and also series made up of rainfall totals of particular months, e.g. one series for a station is composed of 82 terms and each term is the total of the June rainfall, the record extending over 82 consecutive years. Results show that not all the series are stationary and that the non-stationarity has the form of a relatively sharp discontinuity. For most of the series which are stationary the processes do not show a marked departure from random nature. The principal exception is provided by autumn and winter rainfall at Hobart where a periodicity appears and which is still apparent between monthly series after the spectral curves have been subjected to smoothing.