The stationarity of relationships between local and remote climates is a necessary, yet implicit, assumption underlying many paleoclimate reconstructions. However, the assumption is tenuous for many seasonal relationships between interannual variations in the El Nino-Southern Oscillation (ENSO) and the southern annular mode (SAM) and Australasian precipitation and mean temperatures. Nonstationary statistical relationships between local and remote climates on the 31-71-yr time scale, defined as a change in their strength and/or phase outside that expected from local climate noise, are detected on near-centennial time scales from instrumental data, climate model simulations, and paleoclimate proxies.The relationships between ENSO and SAM and Australasian precipitation were nonstationary at 21%-37% of Australasian stations from 1900 to 2009 and strongly covaried, suggesting common modulation. Control simulations from three coupled climate models produce ENSO-like and SAM-like patterns of variability, but differ in detail to the observed patterns in Australasia. However, the model teleconnections also display nonstationarity, in some cases for over 50% of the domain. Therefore, nonstationary local-remote climatic relationships are inherent in environments regulated by internal variability. The assessments using paleoclimate reconstructions are not robust because of extraneous noise associated with the paleoclimate proxies.Instrumental records provide the only means of calibrating and evaluating regional paleoclimate reconstructions. However, the length of Australasian instrumental observations may be too short to capture the near-centennial-scale variations in local-remote climatic relationships, potentially compromising these reconstructions. The uncertainty surrounding nonstationary teleconnections must be acknowledged and quantified. This should include interpreting nonstationarities in paleoclimate reconstructions using physically based frameworks.