Cointegration is an analysis tool for understanding and manipulating non-stationary time series. In previous papers by the authors, application of this econometric methodology to structural health monitoring data has been suggested and investigated. Briefly, if two or more non-stationary time series are cointegrated they can be combined to create a stationary time series purged of the common trends in the original data. This can be particularly useful for purging, for example, temperature dependencies from measured response data, and forming a feature for damage detection that is insensitive to environmental variations. Previous investigations by the authors concern linear cointegration. This paper introduces an approach one might take to 'nonlinear cointegration' that is capable of dealing with both nonstationary and nonlinear time series. Although this topic has previously been addressed by some economists, the authors here attempt a less mathematically rigorous yet practical approach.