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Water resources management and agriculture planning models require a statistical synthesis of some rainfall features, in particular those representing dry atmospheric conditions. The bigger the basin, the more important these features become, as is the case of the La Plata Basin LPB.This paper focuses on the precipitation variability in the large LPB in South America, analysing the number of months per year with low rainfall and the sequences of months with low rainfall, their theoretical distributions and stability, which are needed as input for the models mentioned above.Long time series are used to analyse the lowfrequency variability and the relative importance of decadal variability. Changes are evident in the number of months per year with low rainfall, with a decrease of about 20 in the period after 1970.Theoretical distribution models binomial and geometric are fitted to these empirical distributions, and the regional variability of the fitting parameters is shown. In practically the entire region, the goodnessoffit of the two theoretical models considered is statistically satisfactory.The temporal variability of the parameters of the theoretical binomial p and geometric α distributions is analysed, in excluding subperiods of 10 and 5 years, respectively. The results show lowfrequency variability overlapped on a decadal variability, with low homogeneous regional behaviour.The distribution models have proven to be efficient for frequency adjustments of the rainfall properties studied. These results are an acceptable and necessary input to decision models in LPB. They also make it possible to infer effects of climate change. Copyright © 2008 Royal Meteorological Society [ABSTRACT FROM AUTHOR]