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The aim of this paper is to present recent contributions extending the classical concept of cointegration to non-linear cases. Thus, we look at a joint study of non-stationary and non-linear phenomena and offer a complete presentation of theoretical developments involving the concepts of integration, memory and non-linear cointegration. Within this framework we look at the methods available to express the non-linear cointegration concept: non-linear error correction models, tools developed from information theory and the concepts of mixed time series and time series with strong dependence. The article also gives a brief overview of empirical literature.