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Highlights • The internal relationship between decoupling theory and EKC hypothesis was studied. • A two-dimensional decoupling theory was established. • China and US were taken as a case to study. Abstract The current decoupling theory cannot distinguish the decoupling state of a region with different economic development level. To overcome this problem, this paper first studies the internal relationship between decoupling theory and EKC hypothesis. Furthermore, we establish a two-dimensional decoupling theory of economic development and CO 2 emissions. Finally, taking China and US as a case, this theory is used to explore the decoupling relationship between economic development and CO 2 emissions over the period 1965–2016. If the EKC curve satisfies the inverted U type characteristic, the critical point between strong decoupling and weak decoupling can be approximately obtained at the extreme point of EKC curve. Based on the Tapio decoupling theory and extreme point of EKC curve, the two-dimensional decoupling model with 16 kinds of decoupling sates is established. For China and the United States, the EKC curve of carbon emissions and per capita GDP satisfies the inverted U type characteristic. The threshold value of per capita GDP for China and the United States are $7999.5 and $50980.52, respectively. At present, China's economy is experiencing a low level of economic development. The development of the United States in 2014–2015 and 2015–2016 presented strong decoupling with high level of economic development. [ABSTRACT FROM AUTHOR]