In this study, it is analysed whether the countries with good, moderate, poor and very poor performance according to the Climate Change Performance Index (Bruck, Marten and Bals, 2013) converge towards the average group in terms of emission intensity performance. The aim of the study is to examine whether the countries with same performances in climate change also display similar attitudes in terms of emission intensity performance. As the emission intensity performance index, ratio of the country's share in global emissions release to the share of the country's GDP in global GDP has been used. In the analysis, KSS and AESTAR units root tests based on nonlinear time series analysis techniques have been applied. According to the findings; there is convergence behaviour towards the average in terms of emissions intensity performance for each country group. However, it is noteworthy that, this convergence behaviour is more intense in group of countries with good performance and poor performance. Regarding the convergence behaviour between the groups, only the group average of the countries with moderate performance converges towards the group average of the countries with good performance according to the AESTAR test. However, convergence behaviour does not exist between the group averages according to the ADF and KSS tests. For this reason, in the convergence analysis of the emissions intensity performance, unit root tests based on nonlinear time series technique is more useful than the traditional ADF unit root test.