An investigation into the kinetics of reaction between a diffusing particle and a system of two static spherical sinks is presented. The backward diffusion equation is solved for the probability of reaction with each sink, using both absorbing and radiation boundary conditions. The rate constants for each reaction are also calculated. The reactivity of the sinks is shown to be subadditive, and if the sinks are asymmetric the less reactive sink is more strongly affected by the competition. Competitive effects are found to be modeled adequately by using effective reaction radii. The IRT method is shown to have serious defects for such a system because of the correlation of the two sinks. An application to the reaction of OH radicals with thymidine is presented.