This paper examines the hypothesis of stochastic convergence for two air pollutants emissions (carbon dioxide [CO₂] and sulfur dioxide [SO₂]). The value-added of this paper lies in the use of a recent, alternative econometric method, a pair-wise approach that considers all the possible pairs of log per-capita pollutant emission gaps across all the countries in the sample. In this method, all emissions differences must be stationary around a constant mean. Empirical results support different conclusions on stochastic convergence in per capita CO₂ and SO₂ emissions depending on the choice of the unit root test. The use of specific critical values from the ADF-KPSS joint test overcomes these initial conflicting results and leads to small percentages of stationary pairs around a constant mean; which invalidate the hypothesis of stochastic convergence for per capita emissions of CO₂ and SO₂, even over the OECD sub-dataset.