Fossil fuel combustion generates both CO2 and SO2. CO2 is the most important greenhouse gas; SO2 can cause serious local pollution. But it can alleviate the potential global warming because of negative radiative forcing. Such a phenomenon can be characterized as negatively correlated local and global stock externalities. In this paper, we set up an optimal control problem of negatively correlated local and global stock externality provision. The efficiency conditions for this problem are derived. These conditions modify the Samuelson rules for optimal provision of externalities. In addition, we examine several policy related scenarios of negatively correlated local and global stock externality provisions. Finally, we discuss policy implications and limitation of the theoretical results derived in this paper. We also indicate applications of the theoretical results here to empirical research, particularly to economic analysis of multiple-gas issues in climate change.