This paper reports the formulation of theories of nonhomogeneous kinetics based on the independent pairs approximation for systems where geminate recombination competes with scavenging by a (cylindrical model) macromolecule, The theory describes the spatial distribution of hits on the cylinder and is tested by comparison with Monte Carlo random Rights simulation. The kinetics, the hit distribution, and the distribution of the separation between successive hits modeled by the independent pairs theory are in good agreement with the simulations. Some discrepancies are found, which originate from a three-body correlation effect. The origin of this effect, which may be important in understanding radiation damage in biological systems, is discussed in detail.