General and exact relationships within the nonlocal (pair-site) reactivity context are explicitly derived in the framework of density functional theory. The equations are expressed in terms of linear response functions and associated kernels of the Fukui function and its derivatives with respect to the electron number at constant external potential. It is shown that under a local approximation for the general nonlocal pair-site kernels, the nonlocality character of the chemical response must appear only implicitly through the changes in the chemical potential of the system. In the framework of a more general nonlocal reactivity theory, new relations can be written through the incorporation of more spatial coordinates. The case of a three-site equation between Fukui functions has been explored.