The aim of this paper is to develop two indices for quantifying common but differentiated responsibilities (CBDR) and respective capabilities (RC) of countries in mitigating climate change. These composite indices can help facilitate fair allocation of GHG emission reduction responsibilities across countries. Indices are formulated by taking into account the economic, environmental, social, and technical indicators of a given country. These indicators are usually highly correlated. An index using these indicators must take this high correlation into account, otherwise it will either over or underestimate the responsibility and the capability of a country. This study takes the correlation between the indicators into account in developing the CBDR and RC indices via the principal components method. However, the novelty of this study arises from measuring and using economic, social, technical, and environmental indicators together in creating the composite indices. The CBDR and RC are constructed for 50 countries that are responsible for at least 81% of global GHG emissions, including OECD countries and emerging economies. The Cluster Analyses are employed to classify the countries according to their CBDR and RC scores. The results suggest revision of current responsibility and capability classifications of the UNFCCC.