Diffusion-controlled reactions between particles and a nondilute system of sinks are studied. It is shown that in time-dependent situations it is necessary to take account of retardation effects in the building-up of correlations between competing sinks. The retardation leads to a frequency dependence of the rate coefficient. We derive corrections to the dilute limit value of the rate coefficient in the low concentration, low frequency regime. As an application we consider the effect on the time dependence of a quenching process.