House prices have been moving up strongly in real terms since the mid-1990s in the majority of OECD countries, with the ongoing upswing the longest of its kind in the OECD area since the 1970s. If interest rates were to rise significantly, real house prices may be at risk of nearing a peak. The historical record suggests that the subsequent drops in prices in real terms might be large and that the process could be protracted. To quantify the probability that a peak is nearing in the current situation a probit model was estimated for the period 1970-2005 on a restricted set of what are generally agreed to be the main explanatory variables. Aside from interest rates, these include measures of overheating, such as the gap between real house prices and their long-run trend and the rate of change in real house prices in the recent past. The main finding is that an increase in interest rates by about 1 to 2 percentage points would result in probabilities of a peak nearing of 50% or more in the United States, France, Denmark, Ireland, New Zealand, Spain and Sweden.