The Southern Oscillation index (SOI) can yield information about subsequent streamflows on the South Island of New Zealand; however, the relationship between streamflow and SOI may be nonlinear and heteroscedastic. To deal with such difficulties, the conditional probability of streamflow's being below a critical magnitude, given a prior observation of SOI, can be considered a random variable, with its probability density function (pdf) estimabed by Bayesian analysis of existing observations of streamflow and SOI. The conditional pdf can yield a probabilistic forecast of critically low streamflows given a precursor value of SOI. In the Clutha River basin of New Zealand, average austral summer inflow to the headwater lakes has an unconditional probability of nonexceedance of 360 m3/s of approximately 17%. However, during a moderate La Ni¿a, average austral spring SOI=12, the conditional probability of nonexceedance has an expected value of 55%. Foran El Ni¿o with a spring SOI of -12, the expected probability of nonexceedance is 18%; for a neutral SOI of 0, the expected probability is 10%. Thus, the probability of nonexceedance of seasonal streamflow can be seen to vary by a factor of more than 5 as a function of the SOI. ¿ American Geophysical Union 1994