The Smoluchowski theory describes the kinetics of trapping of Brownian particles by absorbers randomly placed without correlations between their positions. We generalize this theory to take trap correlations into account when traps occur in spherical clusters distributed in space in a noncorrelated manner. A cluster contains n traps uniformly distributed within the cluster. An effective medium treatment is used to handle trap-correlation effects. Explicit expressions are obtained for the time-dependent rate coefficient and the particle survival probability valid for the entire range of n and cluster radius R. We analyze how the trap clustering manifests itself in the kinetics. In particular, we show that there exists a domain of the parameters n and R, where the kinetics is well fitted by a stretched exponential function for more than 99% of the decay. Such behavior should be contrasted to the essentially exponential kinetics predicted by Smoluchowski theory for noncorrelated traps.